CENTRIFUGAL  FANS 

A  THEORETICAL  AND  PRACTICAL  TREATISE 


Fans  for  Moving  Air  iw^La^e^  Quantities 
At  Comparatively  Low  Pressures. 

BY 

J.  H.  KINEALY,  M.  Am.  Soc.  M.  E. 

Formerly   Professor  'of  Mechanical  Engineering  at  Washington  Univer- 

sity, St.  Louis;  Past-president  American  Society  of  Heating  iznd 

Ventilating  Engineers;  Past-president  Engineers'1  Club  of 

St.  Louis;  Member  Society  of  Arts,  England;  Mem- 

ber Boston  Society  of  Civil  Engineers,  etc. 


Net  BooK. 

€L  This  book  is  supplied  to  the  trade 
on  terms  which  do  not  allow  them  to 
give  a  discount  to  the  public. 


NEW  YORK: 
SPON  &  CHAMBERLAIN,  123  Liberty  Street. 

LONDON: 
E.  &  F.  N.  SPON,   LIMITED,  57  Haymarket,  S.  W. 

1905. 


CENTRIFUGAL  FANS. 

A  THEORETICAL  AND  PRACTICAL  TREATISE 

ON1   >^  :   >l   '     '' 

Fans  for  Moving  Air  •  H^  kal^e^ Quantities 
At  Comparatively  Low  Pressures. 

BY 

J.  H.  KINEALY,  M.  Am.  Soc.  M.  E. 

Formerly  Professor  of  Mechanical  Engineering  at  Washington   Univer- 
sity^ St.  Louis;  Past-president  American  Society  of  Heating  and 
Ventilating  Engineers;  Past-president  Engineers'*  Club  of 
St.  Louis;  Member  Society  of  Arts,  England;  Mem- 
ber Boston  Society  of  Civil  Engineers,  etc. 


Fully  Illustrated  and  with  Numerous  Tables  for  Facilitating 
Calculations  in  Regard  to  Fans. 


NEW  YORK: 
SPON  &  CHAMBERLAIN,  123  Liberty  Street. 

LONDON: 
E.  &  F.  N.  SPON,  LIMITED,  57  Haymarket,  S.  W. 

1905. 


n  ^ 


Entered  according  to  Act  of  Congress  in  the  year  1904 

by 

J.  H.  KINEALY 

In  the  Office  of  the  Librarian  of  Congress,  Washington,  D  C. 
Entered  at  Stationers'  Hall. 


t 


Mcllroy  &  Emmet,  Printers,  22  Thames  St.,  New  York. 


PREFACE. 


The  matter  set  forth  in  this  book  was  included 
in  a  series  of  articles  written  for  the  Engineering 
Review  at  the  request  of  its  editor.  The  favorable 
attention  which  the  articles  attracted  lead  the 
author  to  believe  that  there  was  a  real  demand 
for  a  book  treating  in  a  theoretical  as  well  as  a 
practical  way  of  centrifugal  fans.  Hence  the  ar- 
ticles which  appeared  in  the  Engineering  Review 
have  been  thoroughly  revised,  added  to,  and  made 
as  complete  as  possible  for  presentation  to  the 
public. 

The  subject  of  centrifugal  fans  has  been  dealt 
with  by  other  writers,  but  the  author  has  felt  that 
the  method  of  treatment  has  been  in  some  in- 
stances entirely  too  theoretical  and  in  other 
instances  too  intensely  practical.  Some  writers 
have  devoted  their  energies  to  evolving  long  com- 
plicated mathematical  formulas,  which  were  of 
little  or  no  use  to  the  engineer  as  they  always  con- 
tained constants  to  which  the  writers  seemed 
unable  to  assign  specific  values.  As  a  species  of 


IV  PREFACE. 

mental  gymnastics  the  treatises  were  good,  but  as 
an  aid  to  an  .engineer  in  laying  out  a  system  of 
heating  and  ventilating  they  were  of  little  use. 

Other  writers  have  made  certain  statements  in 
regard  to  fans  without  giving  any  explanation  or 
reason  for  their  statements.  They  have  assumed 
the  position  of  knowing  whereof  they  speak,  with- 
out giving  any  evidence  that  they  really  possess 
the  knowledge  they  assume  to  have. 

The  author  has  tried  to  avoid  being  only  theo- 
retical, but  at  the  same  time  has  been  careful  to 
give  a  reason  for  every  statement.  Where  mathe- 
matics has  been  needed,  it  has  been  used,  and 
used  as  freely  as  the  occasion  demanded.  No 
pains  have  been  spared  to  explain  fully  the  entire 
theory  of  centrifugal  fans  and  to  show  clearly  the 
way  in  which  every  formula  and  rule  is  derived. 

In  the  theoretical  matter  and  the  derivation 
of  the  various  formulas  the  author  has  had  in 
mind  the  student  and  the  mathematician,  and  has 
endeavored  to  show  how  the  theory  of  the  vortex 
applies  to  and  is  used  every  day  in  one  branch 
of  engineering.  The  development  of  the  theory 
of  vortexes  as  applied  to  fans  is  the  result  of  sev- 
eral years  of  study  and  work,  and  to  those  who 
wish  to  indulge  in  mental  gymnastics  of  a  mathe- 
matical kind  the  author  recommends  a  study  of 
the  vortex  with  an  inward  flow.  This  is  the  kind 
of  a  vortex  that  one  sees  when  water  flows  out  of 


PREFACE.  V 

a  circular  bowl  through  a  hole  in  the  middle  of 
the  bottom. 

For  the  practicing  engineer  tables  have  been 
prepared,  and  they  have  been  arranged  in  the  way 
which  the  experience  of  the  author  in  designing 
heating  and  ventilating  plants  has  shown  to  be 
most  convenient.  The  tables  are  full  and  com- 
plete, and  it  is  hoped  that  few  typographical 
errors  have  crept  in.  The  calculations  were  care- 
fully made  and  checked,  and  the  proofs  have  been 
carefully  read,  but  even  in  spite  of  care  the  author 
fears  that  here  and  there  some  error  will  be  found, 
and  he  will  be  grateful  to  those  who  call  his  at- 
tention to  any  which  they  may  find. 

The  author  hopes  that  the  book  will  find  as 
much  favor  in  the  eyes  of  the  public  as  did  the 
articles  in  the  Engineering  Review,  and  trusts  that 
it  will  be  of  interest  to  those  who  desire  to  study 
the  theory  of  centrifugal  fans,  and  of  aid  and 
value  to  those  engineers  who  have  to  plan  or  erect 
works  where  fans  must  be  used. 

J.    H.    KlNEALY. 

St.  Louis,  Mo.,  January,  1905 


CONTENTS  OF  CHAPTERS. 


CHAPTER  I. 

PAG] 

Flow  of  air " 

Volume  of  air  flowing 

Pressure  necessary  for  required  velocity 1  \ 


CHAPTER  II. 

Vortex 1.' 

Vortex  with  radical  flow 2! 


CHAPTER  III. 

Fans 2' 

First  type  of  fans 21 

Second  or  Guibal  type  of  fans 3< 

Third  type  of  fans 3< 

Modern  type .  4^ 


Vlll  CONTENTS    OF    CHAPTERS. 

CHAPTER   IV. 

PAGE 

Fan  wheel 51 

Vanes  or  floats 53 

Inlet 60 

Width..  01 


CHAPTER  V. 

Capacity 64 

Blast  area 74 

Effect  of  outlet  on  capacity 78 

Air  per  revolution 87 


CHAPTER  VI. 

Pressure 91 

Work.  .  99 


CHAPTER  VII. 

Horse  power  required  to  run  a  fan 108 

Engine  required  to  run  a  fan 115 

Motor  required  to  run  a  fan 121 

Width  of  belt..  .  124 


CHAPTER  VIII. 

Efficiency 1 28 

Air  per  horse  power 138 


CONTENTS    OF    CHAPTERS.  IX 

CHAPTER   IX. 

PAGE 

Exhausters 143 


CHAPTER  X. 

Housing 147 

Dimensions  of  housings 159 

Shaft.  .  .  168 


CHAPTER  XI. 
Cone  wheels.  .  .170 


CHAPTER  XII. 

Disk  fans 1  SO 

Number  of  revolutions  per  minute 187 

Capacity  of  a  disk  fan 188 

Horse  power  reqtiired 190 


CHAPTER  XIII. 
Choosing  a  centrifugal  fan 197 


CONTENTS  OF  TABLES. 


TABLE  I,  page  4. 

Velocity  in  feet  per  ininue  of  air  for  various  pr  ssures  per 
square  inch. 

TABLE  II,  page  71. 

Capacities  of  fans  with  inlets  whose  diameters  are  0.707 
of  the  diameters  of  the  wheels. 

TABLE   HA,   page  71. 

Capacities  of  fans  with  inlets  whose  diameters  are  O.b25 
of  the  diameters  of  the  wheels. 

TABLE  III,  page  77. 
Blast  areas  in  square  feet  and  square  inches. 

TABLE  IV,  page  85. 
Values  of  the  fraction  — 


V 


AC- 


V, page  89. 
Cubic  feet  of  air  delivered  per  revolution. 


Xll  CONTENTS    OF    TABLES. 

TABLE  VI,  page  93. 

Number  of  revolutions  for  different  pressures  in  ounces 
per  square  inch. 

TABLE   VII,   page  96. 

1  -l-r2 

Values  of  the  fraction   .-    1"t"   ,    , 


TABLE  VIII,  page   110. 

Horse  power  required  to  run  a  fan  when  working  at  its 
capacity  under  different  pressures,  when  the  inlet 
is  0.707  of  the  diameter  of  the  wheel. 


TABLE  VIIlA,  page   110. 

Horse  power  required  to  run  a  fan  when  working  at  its 
capacity  under  different  pressures,  when  the  inlet  is 
0.625  of  the  diameter  of  the  wheel. 


TABLE  IX,  page   120. 
Mean  effective  pressures  for  different  boiler  pressures. 

TABLE  X,  page   125. 
Horse  power  transmitted  by  single  belts. 

TABLE   XA,  page   125. 
Horse  power  transmitted  by  double  belts. 

TABLE  XI,  page  132. 

Efficiency    for   different    ratios    of   diameter   of   inlet    tc 
diameter  of  fan  wheel. 


CONTENTS    OF   TABLES.  Kill 

TABLE  XII,  page   142. 
Air  delivered  per  minute  per  horse  power. 

TABLE  XIII,  page   161. 

Dimensions  of  housings  of  full  housed,  top,  horizontal  dis- 
charge fans,  for  r  equal  0.707. 

TABLE  XIV,  page   162. 

Dimensions   of  housings   of   three    quarter   housed,    top, 
horizontal  discharge  fans,  for  r  equal  0.707. 

TABLE  XV,  page    163. 

Dimensions  of  housings  of  three  quarter  housed,  bottom, 
horizontal  discharge  fans,  for  r  equal  0.707. 

TABLE  XVI,  page   164. 

Dimensions  of  housings  of  full  housed,  top,  horizontal  dis- 
charge fans,  for  r  equal  0.625. 

TABLE  XVII,  page   165. 

Dimensions  of  housings  of  three  quarter  housed,  top,  hori- 
zontal discharge  fans,  for  r  equal  0.625. 

TABLE  XVIII,  page   166. 

Dimensions  of  housings  of  three  quarter  housed,  bottom, 
horizontal  discharge  fans,  for  r  equal  0.625. 

TABLE  XIX,  page   176. 
Capacities  of  cone  wheel  fans. 


TABLE  XX,  page  176. 
Horse  power  required  to  run  cone  wheels. 


XIV  CONTENTS    OF    TABLES. 

TABLE  XXI,  page   195. 

Revolutions  per  minute,  capacity,  working  capacity  and 
horse  power  required  for  disk  fans  with  straight 
plane  blades. 


TABLE  XXII,  page   195. 

Revolutions  per  minute,  capacity,  working  capacity  and 
horse  power  required  for  disk  fans  of  the  Blackinan 
type. 


CHAPTER  I. 


Flow  of  Air.  When  air  or  any  similar  gas 
flows  from  a  vessel  into  a  space  where  the  pressure 
is  not  more  than  five  per  cent,  less  than  the  pres- 
sure in  the  vessel,  the  velocity  per  minute  at 
which  the  air  or  gas  ought  to  flow  if  there  be  no 
friction  is 

(1)  .   5gjp  =  60x/~2~g^ 

v  is  the  velocity  in  feet  per  minute ;  h  is  the  height 
in  feet  of  a  column  of  the  air  or  gas,  having  a 
base  of  one  square  foot,  whose  weight  is  equal  to 
the  difference  between  the  pressures  per  square 
foot  inside  and  outside  the  vessel;  and  g  is  the 
number  32.2,  which  represents  the  acceleration  in 
feet  per  second  of  a  freely  falling  body. 

In  all  work  connected  with  fans  or  blowers 
it  is  customary  to  express  the  pressures  of  air  in 
ounces  per  square  inch.  Therefore  if  d  be  the 


CENTRIFUGAL    FANS. 


density  of'rweigkt<  i'n  pounds  of  one  cubic  foot  of 
-the-  aftf  Un'dei;  consideration;  and  p  be  the  pressure 
in  ounce's'  pet  square'  inch  equivalent  to  the  height 
h  of  the  column  of  air.  we  have 


If  we  put  this  expression  for  &  in  (1)  and  also 
put  for  g  its  value,  we  have 


••Ji 


(2),  -  60V  _  1443 


From  (2)  it  is  seen  that  when  air  flows  from  a 
vessel  into  a  space  in  which  the  pressure  is  p 
ounces  less  than  in  the  vessel,  the  velocity  in  feet 
per  minute  depends  not  only  upon  the  difference 
in  pressures,  p,  but  also  upon  the  density  of  the 
air.  Further,  it  is  seen  that  the  greater  the  den- 
sity the  less  the  velocity,  and  the  less  the  density 
the  greater  the  velocity.  The  density  of  air  varies 
with  the  temperature:  the  higher  the  temperature 
the  less  the  density.  And  hence  (2)  shows  that 


FLOW   OF    AIR.  3 

air  at  a  high  temperature  will  have  a  greater 
velocity  of  flow,  for  the  same  value  of  p,  than  air 
at  a  lower  temperature.  The  density  of  dry  air 
at  32°  is  0.0807,  and  this  value  in  (2) 'gives  as  the 
expression  for  the  velocity  of  flow  of  air  at  32°, 


v  -  5081  Vy 

The  density  of  dry  air  at  100°  is  0.0710,  and 
with  this  value  of  d  the  expression  for  v  is 

v  =  5417  x/7" 

The  writer,  in  his  practice,  usually  assumes  that 
(3)  v  =  5200 


which  corresponds  to  a  value  of  0.0770  for  d, 
which  is  the  density  of  air  at  a  temperature  of  56°. 
This  expression  while  rigidly  true  only  for  a  tem- 
erature  of  56°  and  for  dry  air  is  true  enough  for 
all  practical  purposes  for  ordinary  air  and  any  tem- 
perature between  32°  and  100°,  and  it  has  the  fur- 
ther advantage  of  being  simple  and  easily  remem- 
bered. 

Sometimes  pressures  of  air  in  fan  work  are  ex- 
pressed in  inches  of  water  instead  of  ounces.  And 
as  one  ounce  per  square  inch  is  equivalent  to  a 
head  of  1.73  inches,  to  convert  pressures  in  ounces 


4  CENTRIFUGAL    FANS. 

per  square  inches  to  inches  of  water,  it  is  neces- 
sary to  multiply  the  pressure  in  ounces  by  1.73, 
Also,  to  convert  inches  of  water  to  ounces  per 
square  inch,  divide  the  inches  of  water  by  1.73. 

Table  I.  gives  the  velocity  in  feet  per  minute 
of  air  as  calculated  by  equation  (3)  for  various 
pressures  in  ounces  per  square  inch. 


TABLE  I. 
Velocities  in  feet  per  minute. 


p 

V 

P 

v                    p                    v 

Pressure 

Velocity 

Pressure 

Velocity  in 

Pressure 

Velocity  in 

in  ounces 

in  feet  per 

in  ounces 

feet  per 

in  ounces 

feet  per 

per  sq.  in. 

minute 

per  sq.  in. 

minute 

per  sq.  in. 

minute 

0.0 

0 

0.75 

4500              3.0 

9000 

0.1 

1645 

0.8 

4650              3.5 

9720 

0.2 

2325 

0.9 

4940 

4.0 

10400 

0.25 

2600 

1.0 

5200 

5.0 

11600 

0.3 

2850 

1.25 

5810 

6.0 

12700 

0.4 

3290 

1.5 

6370 

7.0 

13800 

0.5 

3680 

1.75 

6880 

8.0 

14700 

0.6 

4030 

2.0 

7350 

9.0 

15600 

0.7 

4350 

2.5 

8220 

10.0 

16400 

Volume  of  Air  Flowing.  It  is  evident  that  if 
the  area  in  square  feet  of  the  opening  through 
which  an  air  or  gas  flows  be  multiplied  by  the 
velocity  in  feet  per  minute,  the  quotient  ought  to 
be  the  volume  of  the  air  which  flows  out  per  min- 
ute. Unfortunately,  however,  experiments  show 
that  when  a  gas  flows  through  an  opening  in  the 
side  of  a  vessel  the  quantity  that  actually  flows 


VOLUME    OF    AIR  FLOWING. 


5 


out  per  minute  is  less  than  the  theoretical  amount 
which  the  size  of  the  opening  and  the  difference 
in  pressures  would  indicate  ought  to  flow.  This 
reduction  in  the  quantity  is  due  to  two  causes: 
First  it  is  found  that  there  is  a  reduction  in  the 


FIG.  1. 


area  of  the  cross-section  of  the  stream  flowing  out, 
so  that  its  area  of  cross-section  where  the  velocity 
Is  greatest  is  not  equal  to  the  area  of  the  opening; 
and  second,  the  actual  velocity  is  somewhat  less 
than  the  theoretical  velocity  because  of  friction. 


O  CENTRIFUGAL    FANS. 

The  reduction  of  the  area  of  the  cross-section 
of  the  stream  of  issuing  gas  and  also  the  reduction 
of  the  velocity  depends  upon  the  kind  of  outlet 
through  which  the  gas  flows.  If  the  outlet  is  in  a 
thin  wall  the  shape  of  the  issuing  stream  is  as 


FIG.  2. 


shown  in  Fig.  1,  where  the  converging  lines  indicate 
the  flow  of  the  issuing  gas,  before  it  reaches  the 
outlet.  When  the  orifice  is  a  short  projecting 
tube,  the  form  of  the  stream  is  as  shown  in  Fig.  2. 
If  the  tube  projects  inside  of  the  side  of  the  vessel 


VOLUME   OF    AIR    FLOWING.  7 

the  form  of  the  stream  is  as  shown  in  Fig.  3.  And 
if  the  tube  is  conical  shaped  the  flow  is  as  shown 
in  Fig.  4.  In  all  cases  the  velocity  of  the  flow  is 
greatest  at  the  smallest  section  which  is  always 
of  less  area  than  the  mouth  of  the  outlet.  The 


FIG.  3. 


greatest  velocity  is  usually  almost  but  not  quite 
equal  to  the  theoretical  velocity  due  to  the  pres- 
sure making  the  gas  flow  out. 

If  then  a  is  the  area  in  square  feet  of  an  opening 
through  which  air  or  gas  flows,  and  v  is  the  velocity 


8 


CENTRIFUGAL    FANS. 


in  feet  per  minute  of  the  flow  as  calculated  by 
equation  (3),  the  quantity  Q  in  cubic  feet  which 
will  flow  out  per  minute  is 


(4) 


Q  =  c  av 


c  is  called  the  coefficient  of  discharge,  and  is  the 
ratio  of  the  actual  discharge  to  the  theoretical. 


FIG.  4. 


It  is  exceedingly  difficult  to  give  an  exact  value 
to  c  except  for  those  particular  conditions  and 
size  of  openings  which  have  been  used  in  making 
experiments,  and  even  for  those  conditions  which 
are  almost  alike  different  experimenters  have  ob- 
.  tained  different  results.  In  -some -eases  c  is  due 


VOLUME    OF    AIR    FLOWING. 

almost  wholly  to  a  reduction  of  velocity,  and  in 
others  to  the  fact  that  the  cross-section  of  the 
stream  of  discharge  where  it  has  its  maximum 
velocity  is  much  less  than  the  actual  area  of  the 
opening  in  the  vessel.  The  fact  is  that  in  choos- 
ing the  proper  value  of  c  to  be  used  in  any  par- 
ticluar  case  it  is  necessary  to  exercise  a  great  deal 
of  that  particular  sense  or  judgment  which  goes 
with  and  makes  the  successful  engineer. 

For  a  circular  opening  in  a  thin  plate  or  a 
plate  whose  thickness  is  small  compared  to  the 
diameter  of  the  opening,  c  may  be  taken  as  0.62. 

For  a  circular  tube  projecting  from  the  flat 
side  of  a  vessel,  when  the  length  of  the  tube  is 
between  1.5  and  2.5  times  the  diameter  of  the 
tube,  c  may  be  taken  as  0.82. 

For  a  short  tube  which  projects  into  the  vessel 
instead  of  out  of  it,  c  may  be  taken  as  0.50. 

For  a  conical  shaped  tube  whose  length  is 
about  5.5  the  smaller  diameter,  whose  large  diam- 
eter is  about  1.3  the  small  diameter,  when  the 
flow  is  from  the  larger  diameter  towards  the 
smaller,  and  when  the  area  of  the  smaller  end  of 
the  tube  is  used  in  calculating  the  discharge,  c 
may  be  taken  as  0.94. 

For  a  square  opening  c  may  be  taken  the  same 
as  for  a  circular  opening  whose  diameter  is  equal 
to  the  side  of  the  square. 

•The  value  of  c  for  a  rectangular  opening  which 
is  not  a  square  depends  upon  the  relation  of  the 


10  CENTRIFUGAL    FANS. 

two  sides,  and  it  is  impossible  to  give  any  short 
rule  for  determining  it. 

It  is  evident  that  it  makes  no  difference  as  to 
the  actual  result  of  our  calculation  whether  we 
say  that  c  is  due  to  a  reduction  of  velocity  as  well 
as  to  a  reduction  of  the  area  of  the  stream  flowing 
out,  or  whether  we  assume  simply  for  the  purposes 
of  calculation  that  c  is  due  entirely  to' a" reduction 
of  velocity.  The  result  of  the  calculation  will  be 
exactly  the  same  in  either  case.  When  the  pres- 
sure under  which  the  air  flows,  and  the  area  of  the 
outlet  are  both  known,  all  that  is  necessary  is  to 
determine  the  velocity  of  the  flow  by  equation  (3) 
or  Table  I.  and  multiply  it  by  the  area  of  the 
opening  and  the  proper  value  of  c. 

EXAMPLE: — How  many  cubic  feet  of  air  will 
flow  per  minute  through  a  circular  opening  2  feet 
in  diameter  in  the  side  of  an  iron  tank  in  which 
the  pressure  is  2  ounces? 

Here  a,  the  area  of  the  outlet,  is  3.14  square 
feet.  And  from  Table  I.  it  is  seen  that  v,  the 
velocity  of  the  air  flowing  out,  is  7350  feet  per 
minute.  The  thickness  of  the  metal  of  the  tank 
will,  of  course,  be  small  as  compared  to  the  diam- 
eter of  the  opening  in  this  case  and  therefore  we 
take  c  as  0.62. 

These  values  of  a,  v,  and  c  in  equation  (4)   give 

Q  =  cav  =  0.62x3.14x7350  =  14300. 


PRESSURE  NECESSARY  FOR  A  REQUIRED  VELOCITY. 

Pressure  Necessary  for  a  Required  Velocity.     In 

what  has  been  said  before  it  has  been  assumed 
that  the  pressure  is  known  and  that  the  velocity 
or  the  quantity  of  flow  is  to  be  found.  In  many 
cases,  however,  the  velocity  or  the  quantity  is 
given  and  it  is  required  to  find  the  necessary  pres- 
sure. 

From  equation  (3)  we  get  the  following  equa- 
tion for  determining  the  pressure  in  ounces  per 
square  inch  necessary  to  give  a  velocity  or  flow 
of  v  feet  per  minute. 

r  v  T 

(5>         *  =  [5200] 

When  we  have  given  the  quantity  of  air  Q 
which  is  to  flow  per  minute  from  the  vessel  and 
also  the  kind  of  outlet  we  can  determine  v  by  the 
following  equation  which  comes  from  (4), 


(6)  »/•",' 

ca 


Then  knowing  v  we  use  equation  (5)  to  find  p 
or  we  may  substitute  in  (5)  the  value  of  v  as 
given  by  (6)  and  get  at  once  the  following  ex- 
pression for  p,  without  determining  v  at  all. 


*  - 


12  CENTRIFUGAL    FANS. 

If  the  coefficient  of  discharge  were  equal  to 
one,  that  is,  if  there  were  no  reduction  in  either 
the  velocity  or  the  area  of  the  outlet,  the  quantity 
actually  discharged  would  be  equal  to  the  theoret- 
ical quantity,  and  the  expression  for  p  would  be 


(8) 


r  Q  T 

_  5200a  J 


If  we  divide  equation  (7)  by  equation  (8)  we 
get  the  ratio  of  the  theoretical  pressure  to  give  a 
required  velocity  or  to  produce  a  given  flow,  to 
the  actual  pressure  necessary.  This  ratio  may  be 
designated  F,  and  its  value  is 


_ 

5200oc 


EXAMPLE: — What  is  the  theoretical  and  the 
actual  <  pressure  required  in  order  to  discharge 
8000  cubic  feet  of  air  per  minute  through  a  short 
circular  tube  whose  area  of  cross-section  is  1  square 
foot?  :  .;.  •  • 

Here  Q  is  8000;  a  is  1,  and  c  for  a  short  tube, 
may  be  taken  as  0.82.  From  (8)  we  have  the 
theoretical  pressure  is 


PRESSURE  NECESSARY  FORA  REQUIRED  VELOCITY.    1;3 


__ 

L5200  x  1J 
And  from  (7)  we  have  the  actual  pressure  is 


80°°  T   -352 

~~ 


That  is,  the  theoretical  pressure  required  is 
2.37  ounces,  while  the  actual  pressure  is  3.52 
ounces.  The  difference  is  what  is  lost  by  friction 
and  the  cohesion  of  the  particles  of  the  air  to  one 
another. 

The  ratio  of  the  actual  pressure  to  the  theoret- 
ical pressure  required  is  3.52  divided  by  2.37  or  1.48. 

We  could  have  determined  this  ratio  by  (9), 
without  having  determined  the  theoretical  and 
actual  pressures,  as  follows, 


1      =1.48 


0.82*          0.674 

In  other  words,  the  actual  pressure  is  nearly 
50  per  cent,  greater  than  the  theoretical  pressure, 
and  this  50  per  cent,  is  simply  lost  in  overcoming 
friction.  There  is  always  this  kind  of  a  loss  when 
air  or  gas  flows  from  one  vessel  into  another,  or 
from  one  space  into  another,  and  the  actual 


14  CENTRIFUGAL    FANS. 

amount  of  the  loss  depends  upon  the  orifice  through 
which  the  air  or  gas  flows.  When  air  flows  into 
the  inlet  of  a  fan  or  from  a  chamber  into  a  pipe 
there  is  this  same  kind  of  a.  loss  which  must  be 
determined  according  to  the  size  and  shape  of  the 
orifice,  and  it  must  be  allowed  for  when  deter- 
mining the  actual  pressure  required  for  the  dis- 
charge of  a  given  quantity  of  air  per  minute. 


CHAPTER  II. 


Vortex.  If  a  cylindrical  vessel  such  as  is  shown 
in  Fig.  5  be  partly  filled  with  water  or  any  similar 
liquid  to  the  line  A  B,  and  then  the  water  be  made 
to  rotate,  it  will  be  found  that  the  surface  of  the 
water  will  be  depressed  at  the  center  and  raised 
at  the  circumference  as  shown  in  Fig.  5.  The  cir- 
cumference will  be  raised  the  same  height  above 
the  original  surface  that  the  center  is  depressed 
below  it,  and  the  surface  will  have  the  shape  of  a 
paraboloid  with  its  vertex  at  E  instead  of  the 
horizontal  plane  A  B  as  it  was  before  the  rotation. 
The  surface  of  the  paraboloid  is  represented  in 
Fig.  5  by  the  parabola  C  ED,  and  if  this  parabola 
were  revolved  about  its  vertical  axis  it  would 
generate  the  surface  which  the  water  has  when 
revolved. 

As  long  as  the  water  is  kept  rotating  with  the 
same  velocity  the  surface  will  preserve  the  shape 
of  the  same  paraboloid  C  E  D,  but  the  vertex  E 

15 


16 


CENTRIFUGAL    FANS. 


will  always  for  all  velocities  of  rotation  be  the 
same  distance  below  the  original  surface  A  B  that 
the  circumference  C  D  is  above  it.  The  distance 


A 


B 


FIG.  5. 


that  E  is  below  the  surface  A  B  and  the  distance 
that  the  circumference  C  D  is  above  it  depend 
upon  the  velocity  of  rotation  of  the  water,  but 


VORTEX.  17 

they  are  equal  to  one  another  for  all  velocities  of 
rotation. 

This  making  the  surface  of  a  liquid  assume  the 
shape  of  a  paraboloid  by  rotation  constitutes  what 
is  called  a  vortex. 

It  can  be  shown  by  mathematics,  which  would 
be  out  of  place  here,  that  the  distance  of  the  cir- 
cumference C  D  above  the  vertex  E,  is  equal  to , 
the  height,  corresponding  to  h  in  equation  (1), 
necessary  to  give  to  the  particles  of  the  liquid  at 
the  circumference  the  velocity  which  they  have. 
And  every  point  on  the  surface  of  the  rotating 
liquid  is  above  the  lowest  point  E  a  distance  equal 
to  the  height  necessary  to  give  the  liquid  at  that 
point  the  velocity  which  it  has.  The  velocity  of 
rotation  of  the  particles  of  liquid  at  the  center  is 
zero  and  it  increases  from  the  center  towards  the 
circumference  where  it  is  greatest.  After  the 
vortex  is  once  formed,  there  is  no  radial  flow  of 
the  particles  of  water,  they  have  only  a  motion  of 
rotation  about  the  center.  That  is  to  say,  the 
particles  do  not  flow  either  towards  or  away  from 
the  center  after  the  vortex  is  formed,  they  simply 
revolve  about  it.  During  the  formation  of  the 
vortex,  there  is,  of  course,  a  flowing  of  the  par- 
ticles away  from  the  center  towards  the  circum- 
ference, but  this  flow  ceases  as  soon  as  the  vortex 
is  formed. 

The  pressure  per  square  inch  on  the  bottom 
of  the  vessel  is  changed  by  the  rotation  of  the 


18  CENTRIFUGAL    FANS. 

water  and  the  formation  of  the  vortex.  Before 
the  formation  of  the  vortex  the  pressure  per 
square  inch  was  uniform  over  the  whole  bottom 
and  was  that  due  to  the  depth  from  the  surface 
of  the  liquid  to  the  bottom;  but  after  the  vortex 
was  formed  the  pressures  on  different  points  of  the 
bottom  became  different  from  what  they  were 
before  in  exactly  the  same  proportion  that  the 
depths  at  the  different  points  were  changed  by  the 
formation  of  the  vortex.  At  the  center,  cfirectly 
below  E,  the  pressure  becomes  less  than  before 
the  formation  of  the  vortex  by  an  amount  corre- 
sponding to  the  distance  of  E  below  the  original 
surface  A  B.  And  at  the  circumference  the  pres- 
sure becomes  greater  than  before  the  formation  of 
the  vortex  by  an  amount  corresponding  to  the  dis- 
tance of  C  D  above  A  B.  Before  the  formation 
of  the  vortex  the  pressure  at  the  circumference  is 
exactly  the  same  as  that  at  the  center;  but  after 
the  vortex  is  formed,  the  pressure  at  the  circum- 
ference is  greater  than  that  at  the  center  by  an 
amount  corresponding  to  the  distance  of  C  D 
above  E.  But  the  distance  of  C  D  above  E  is,  as 
has  been  stated,  equal  to  the  height  corresponding 
to  the  velocity  of  the  particles  at  the  circumference ; 
and  hence  the  pressure  at  the  circumference  after 
the  formation  of  the  vortex  is  greater  than  the 
pressure  at  the  center  by  an  amount  equal  to  the 
height  which  corresponds  to  the  velocity  of  the 
particles  at  the  circumference. 


VORTEX. 


19 


If  instead  of  an  open  vessel  such  as  is  shown 
in  Fig.  5,  there  be  a  thin  closed  vessel  such  as  is 
shown  in  Fig.  6,  and  it  be  filled  with  a  liquid  and 
then  revolved  about  a  vertical  axis  A  B  passing 
through  the  center,  there  will  be  found  to  be  the 
same  tendency  to  form  a  vortex  that  there  was  in 
the  vessel  of  Fig.  5.  In  this  case,  however,  the 


B 
y  FIG.  6. 

shape  of  the  surface  of  the  liquid  cannot  change 
because  of  the  top  of  the  vessel,  but  the  pressures 
at  various  points  from  the  center  towards  the  cir- 
cumference will  change  in  a  manner  similar  to 
what  they  did  in  the  case  of  Fig.  5.  The  pressure 
on  the  bottom  at  the  circumference  will  be  greater 
than  at  the  center  by  an  amount  exactly  equal 
to  the  height  of  a  column  of  the  liquid  corre- 
sponding to  the  velocity  of  rotation  at  the  cir- 


20  CENTRIFUGAL    FANS. 

cumference.  In  the  same  way  the  pressure 
against  the  top  of  the  vessel  would  change,  it 
would  become  less  at  the  center  and  greater  at 
the  circumference  because  of  the  rotation,  but  the 
difference  between  the  pressure  at  the  center  and 
that  at  the  circumference  will  be  exactly  equal 
to  that  corresponding  to  the  velocity  of  rotation  of 
the  liquid  at  the  circumference. 

•  In  what  has  been  said  nothing  has  been  inti- 
mated as  the  effect  of  friction  or  the  way  in  which 
the  liquid  is  made  to  rotate  in  the  vessel.  The 
effect  of  friction  is  simply  to  make  it  more  difficult 
to  set  the  liquid  to  rotating  and  to  reduce  the 
velocity  of  the  particles  in  direct  contact  with  or 
near  to  the  walls  of  the  vessel.  The  means 
adopted  to  put  the  liquid  in  motion  makes  no 
differenc3  as  to  the  result  or  as  to  the  difference 
between  the  pressures  at  different  points  provided 
the  liquid  is  actually  made  to  rotate.  If,  how- 
ever, the  liquid  be  made  to  rotate  by  means  of  a 
small  paddle  \vheel  such  as  is  shown  in  Fig.  7, 
where  the  diameter  C  D  of  the  vessel  is  greater 
than  the  diameter  A  B  of  the  wheel,  the  velocity 
of  rotation  of  the  liquid  between  the  ends  of  the 
paddles  and  the  circumference  of  the  vessel  may 
be,  and  is  very  likely  to  be,  somewhat  greater  than 
the  velocity  of  the  extremities  of  the  paddles  of 
the  wheel.  That  is  to  say,  because  of  the  adhesion 
of  the  particles  to  the  paddles  some  of  the  par- 
ticles immediately  outside  of  the  wheel  will  be 


VORTEX. 


21 


carried  around  just  as  if  the  diameter  of  the 
wheel  were  greater  than  it  actually  is.  This  ap- 
parent increase  in  the  diameter  of  the  wheel  de- 
pends upon  the  adhesion  of  the  particles  to  one 
another  and  to  the  ends  of  the  paddles.  The 
difference  between  the  pressure  at  the  center  and 
that  at  the  circumference  will  be  equal  to  the  height 


FIG.  7. 

corresponding  to  the  velocity  of  the  liquid  at  the  cir- 
cumference and  not  the  height  corresponding  to  the 
velocity  of  the  tips  of  the  paddles,  although  the  two 
velocities  may  happen  to  be  the  same.  This  is  of 
importance  when  discussing  the  pressure  produced 
in  the  casing  of  a  fan  or  a  centrifugal  pump  when 
the  outlet  is  closed. 

The  results  pointed  out  for  the  rotation  of  a 


22  CENTRIFUGAL    FANS. 

liquid  in  a  closed  vessel  are  exactly  the  same  as. 
those  obtained  when  a  centrifugal  fan  wheel  is  re- 
volved in  its  casing  or  housing  with  either  the 
outlet  or  the  inlet  closed  so  as  to  prevent  the  flow 
of  air  through  the  wheel.  The  diameter  of  the 
\vheel  may  apparently  be  increased  and  the  dif- 
ference between  the  pressure  at  the  center  and 
that  of  the  circumference  may  be  somewhat  greater 
than  that  corresponding  to  the  velocity  of  the 
circumference  of  the  wheel.  If  the  inlet  of  the 
casing  is  closed  and  the  outlet  open,  the  pressure 
at  the  circumference  of  the  casing  will  be  equal 
to  that  of  the  atmosphere,  and  the  pressure  at  the 
center  will  be  less;  while  if  the  inlet  is  open  and 
the  .outlet  is  closed,  the  pressure  at  the  center  will  • 
be  equal  to  that  of  the  atmosphere,  and  the  pres- 
sure at  the  circumference  will  be  greater.  But  in 
both  cases  the  difference  between  the  pressure  at 
the  center  and  that  at  the  circumference  of  the 
casing  will  be  exactly  equal  .to  that  corresponding 
to  the  velocity  of  rotation  of  the  air  at  the  circum- 
ference of  the  casing,  and  the  velocity  of  rotation 
of  the  air  may  be  greater  than  the  velocity  of  rota- 
tion of  the  tips  of  the  blades  of  the  fan. 

Vortex  with  Radial  Flow.  What  has  been  said 
in  the  preceding  article  applies  to  vortexes  in 
which  there  is  n6.  radial  flow,  either  outward  from 
the  center  towards  the  circumference  or  inward 
from  the  circumference  towards  the  center,  but 


VORTEX    WITH    RADIAL    FLOW.  23 

the  whole  motion  of  the  liquid  in  the  vessel  is  one 
of  rotation  about  the  center.  This,  however,  is  not 
the  condition  which  exists  in  a  fan  when  it  is  dis- 
charging air.  Such  a  condition  exists  in  a  fan 
only  when  either  the  inlet  or  the  outlet  is  closed. 
When  a  fan  is  discharging  air  there  is  a  flow  of  air 
outward  from  the  central  part  towards  the  cir- 
cumference, and  the  air  in  the  fan  wheel  has  a 
motion  of  rotation  about  the  center  and  also  a 
radial  motion  from  the  center  towards  the  circum- 
ference. 

As  no  centrifugal  fan  has  been  built  in  which 
the  air  traveled  from  the  circumference  towards 
the  center,  it  is  not  necessary  to  discuss  here  vor- 
tices which  have  a  radial  velocity  inward  towards 
the  center. 

After  a  vortex  is  formed  there  may  be  a  radial 
velocity  of  liquid  from  the  center  towards  the 
circumference  without  effecting  the  vortex  in  any 
way,  provided  that  there  is  no  place  where  the 
radial  velocity  exceeds  the  velocity  of  rotation. 
If  the  radial  velocity  at  any  place  does  exceed  the 
velocity  of  rotation  there  is  a  tendency  at  that 
place  to  break  down  the  vortex,  and  the  pressure 
due  to  the  vortex  is  reduced  at  every  point  by  an 
amount  equal  to  the  height  corresponding  to  the 
difference  in  heads  required  for  the  radial  velocity 
and  the  velocity  of  rotation  at  that  point. 

Now,  in  a  vortex  that  has  an  outward  radial 
flow  the  liquid  enters  near  the  center,  where  the 


24 


CENTRIFUGAL    FANS. 


velocity  of  rotation  is  less  than  at  any  point  far- 
ther out  towards  the  circumference,  and  hence 
what  has  just  been  said  amounts  to  saying  that 
the  velocity  of  radial  flow  at  the  entrance  must 
not  exceed  the  velocity  of  rotation  at  the  en- 
trance. If  the  radial  velocity  at  the  entrance  ex- 
ceeds the  velocity  of  rotation  at  the  entrance,  the 
pressure  at  the  circumference  will  be  less  than  that 
due  to  the ,.  velocity  of  rotation  at  the  circum- 
ference by  an  amount  equal  to  the  difference  be- 
tween the  heads  required  for  the  radial  velocity 
and  for  the  velocity  of  rotation  at  the  entrance. 


B 


This  can  probably  be  made  somewhat  clearer 
by  reference  to  Fig.  8,  which  represents  a  form  of 
vortex -producing  apparatus  working  upon  air. 
That  is  to  say,  it  is  a  fan  whose  inlet  is  C  D.  If 
the  outlet  at  the  circumference  be  closed,  as  indi- 
cated by  the  dotted  lines  A  and  B,  and  the  paddle 
wheel  be  revolved,  there  will  be  no  flow  through 
the  fan,  and  the  pressure  at  the  circumference  will 
be  greater  than  that  at  the  entrance  by  an  amount 
corresponding  to  the  velocity  of  the  air  at  the 
circumference.  Let  this  pressure  be  P. 


1 

1 

\ 

/ 

c 

np 

FK 

i 
',.  8. 

D 

VORTEX    WITH    RADIAL    FLOW.  25 

Now  suppose  an  opening  be  made  at  A  or  B. 
The  air  will  flow  out  of  this  opening  with  a  velocity 
corresponding  to  the  pressure  at  the  circumference, 
and  it  will  enter  the  fan  with  a  radial  velocity  of  a 
certain  amount  depending  upon  the  quantity  of 
air  flowing  through  the  apparatus  per  minute. 
Let  the  pressure  corresponding  to  this  radial  ve- 
locity be  pt  and  let  the  pressure  corresponding  to 
the  velocity  of  the  tips  of  the  paddles  at  the  point 
of  entrance  be  p2.  Then  as  long  as  p1  does  not 
exceed  p2  the  pressure  at  the  circumference  will 
be  P;  but  if  p1  is  greater  than  p2  the  pressure  at 
the  circumference  will  be 


It  has  been  assumed  in  the  preceding  that  the 
velocity  of  radial  flow  is  greatest  at  the  point  of 
entrance,  since  this  assumption  is  in  accordance 
with  the  facts  as  they  actually  exist  in  fans,  as 
will  be  shown  later. 

Hence  if  we  call  p  the  difference  between  the 
pressure  at  the  center  and  that  at  the  circum- 
ference of  a  vortex  having  a  radial  flow,  we  find 
that  its  value  depends  upon  the  condition  of  radial 
flow  as  follows: 

1.  When  the  velocity  of  the  radial  flow  at 
entrance  is  equal  to  or  less  than  the  velocity  of 
rotation  at  entrance 

(10)  p  =  P 


26  CENTRIFUGAL    FANS. 

2.  When  the  velocity  of  the  radial  flow  at 
entrance  is  equal  to  or  greater  than  the  velocity  of 
rotation  at  entrance, 

(11)  p  =  P  +  p2-p, 

It  is  to  be  noticed  that  if  p2  is  equal  to  plt 
equation  (11)  becomes 


which  is  the  same  as  equation  (10). 

Conditions  1  and  2  are  the  only  ones  which 
can  arise  in  the  case  of  vortices  with  an  outward 
radial  flow,  and  the  equations  for  these  conditions, 
that  is,  equations  (10)  and  (11),  are  the  bases  of 
the  equations  used  in  discussing  centrifugal  fans.' 


or  ,T 
VNIVEf 


CHAPTER  III. 


Fans.  Every  centrifugal  fan  may  be  consid- 
ered as  an  apparatus  for  producing  vortexes  of  air 
or  gases  with  a  radial  flow  outward  from  the  cen- 
tral part  towards  the  circumference.  And  the 
more  perfect  are  the  vortexes  produced  the  more 
efficient  as  a  rule  is  the  fan.  The  type  and  pro- 
portions of  a  fan  should  depend  upon  the  work 
it  has  to  do.  If  it  is  intended  for  the  purpose 
of  moving  a  large  quantity  of  air  against  a  com- 
paratively low  pressure  its  proportions  and  general 
construction  should  be  decidedly  different  from 
what  they  should  be  if  it  were  intended  for  the  pur- 
pose of  moving  a  rather  small  quantity  of  air 
against  a  high  pressure.  The  earlier  fans  were  in- 
tended principally  for  the  ventilation  of  mines 
and  they  were  required  primarily  for  moving  large 
quantities  of  air  against  comparatively  low  resist- 
ances. They  were  usually  aspirator  fans  rather 
than  blowers.  That  is  to  say,  they  were  used  for 

27 


28  CENTRIFUGAL    FANS. 

producing  a  partial  vacuum  in  the  air-shaft,  and 
thus  creating  a  flow  of  air  through  it.  They 
usually  discharged  the  air  either  into  a  large 
chamber  surrounding  the  fan  or  directly  into  the 
surrounding  atmosphere.  They  seldom  had  a 
housing  or  casing  about  the  fan  wheel  except  when 
it  was  necessary  to  protect  the  wheels  from  the 
weather.  This  type  of  fans  was  followed  by  a 
type  which  always  had  a  housing  or  casing  sur- 
rounding the  fan  wheel  and  the  fans  could  be 
used  either  as  aspirators  for  creating  a  suction  or 
as  blowers  for  forcing  air  against  a  pressure.  This 
second  type  of  fans  was  followed  by  a  third  type 
which  differed  from  the  second  only  in  the  shape 
of  the  housing  or  casing  and  which  was  the  fore-' 
runner  of  what  may  be  called  the  modern  type  of 
centrifugal  blower  so  much  used  to-day  for  heat- 
ing and  ventilating  work,  for  mechanical  draft  work 
and  in  fact  wherever  it  is  necessary  to  move  large 
quantities  of  air  against  comparatively  small  re- 
sistances. Fans  of  this  last  type  could  be  used 
equally  well  either  as  aspirators  or  blowers. 

It  is  extremely  difficult  to  say  to  whom  be- 
longs the  honor  of  devising  the  first  type  of  cen- 
trifugal fan,  as  the  development  of  these  fans 
seems  to  have  been  almost  identical  as  to  time 
and  character  on  the  continent  of  Europe  and  in 
England.  As  is  usually  the  case  in  every  art, 
men  were  working  on  the  problem  in  different 
places  very  remote  from  one  another  and  were 


FANS.  29 

reaching  pretty  much  the  same  results  by  some- 
what different  methods. 

The  first  type  of  fans  "may  be  considered  as 
represented  by  any  one  of  half  a  dozen  different 
makes  of  fans  erected  in  England  or  Europe  pre- 
vious to  1830. 

The  second  type  of  fans  may  probabty  be 
ascribed  to  the  ingenuity  and  inventive  genius  of 
Guibal  of  France. 

The  third  type  of  fans  was  simply  the  out- 
growth of  the  second  or  Guibal  type.  It  is  hard 
to  say  to  whom  belongs  the  honor  of  its  invention, 
although  it  is  sometimes  spoken  of  as  the  Schiele 
type  of  fans. 

The  First  Type  of  Fans.  This  type  of  fans 
was  always  used  as  an  exhauster  for  moving  air 
by  suction  and  discharging  it  directly  into  the 
atmosphere.  The  fans  were  used  primarily  for 
producing  a  circulation  of  air  for  ventilating  pur- 
poses through  mines.  Before  its  use  mines  had 
been  ventilated  by  creating  an  upward  draft  in 
an  air-shaft  by  means  of  a  fire  at  the  bottom.  The 
fan  was  usually  mounted  on  the  surface  of  the 
ground  near  or  at  the  air-shaft,  with  its  inlet  con- 
nected to  the  outlet  of  the  air-shaft.  When  the 
fan  was  revolved  it  created  a  reduction  of  pressure 
at  the  top  of  the  air-shaft,  which  in  turn  produced 
a  flow  of  air  or  gases  from  th?  mine  below  up  the 
air-shaft  into  the  fan,  by  which  it  was  discharged 


30  CENTRIFUGAL    FANS. 

into  the  atmosphere.  Fans  of  this  type  consisted 
simply  of  a  fan  wheel,  often  without  any  casing 
or  housing  except  what  was  necessary  to  protect 
them  from  the  weather,  and  they  discharged  the 
air  or  gases  directly  into  the  atmosphere  from  all 
points  of  the  periphery  of  the  wheel.  The  wheels 
were  usually  quite  large,  some  even  having  a 
diameter  as  great  as  25  feet.  The  diameter  of  the 
inlet  was  usually  about  -0.6  the  diameter  of  the 
wheel.  The  width  of  the  wheel,  that  is,  the  di- 
mension in  the  direction  of  the  axis,  was  usually 
about  0.50  of  the  diameter  of  the  inlet.  The 
wheel  was  usually  of  a  uniform  width  from  the 
inlet  to  the  circumference.  There  was  always 
only  one  inlet  to  the  fans  of  this  type;  that  is, 
air  was  admitted  to  the  wheel  from  one  side  only. 
The  wheels  could  be  placed  either  in  a  vertical  or  a 
horizontal  position.  When  in  a  vertical  position, 
the  fan  wheel  had  its  axis  horizontal  and  the 
inlet  was  connected  with  the  air-shaft  of  the  mine 
to  be  ventilated  by  a  horizontal  duct.  When  in 
a  horizontal  position,  the  axis  of  the  fan  wheel 
was  vertical  and  the  inlet  was  usually  -placed 
directly  over  the  outlet  of  the  air-shaft. 

The  vanes  or  paddles  of  the  earlier  fans  of  this 
type  were  usually  straight  and  were  placed  ra- 
dially, but  in  the  later  fans  they  were  often  curved. 
It  is  possible  that  to  Combes  belongs  the  honor  of 
first  suggesting  that  the  vanes  of  fans  be  curved. 
He  required  that  the  vanes  of  the  fans  designed 


FIRST    TYPE     OF    FANS.  31 

by  him  be  curved  to  a  very  marked  degree;  other 
designers  required  that  the  vanes  be  curved,  but  not 
to  the  same  shape  recommended  by  Combes. 

The  earlier  fans  of  this  type  usually  had  but 
one  movable  disk  which  carried  the  vanes,  and 
the  fan  was  placed  so  that  the  vanes  moved  close 
to  a  stationary  wall  on  the  inlet  side  of  the  wheel. 
The  movable  disk  was  fastened  to  the  shaft  and 
extended  out  to  the  circumference  of  the  wheel. 
The  later  fans  had  two  movable  disks  between 
which  the  vanes  were  fixed  as^in  the  modern  fans. 
One  of  these  disks  extended  from  the  shaft  to  the 
circumference  of  the  wheel,  while  the  other,  on 
the  inlet  side  of  the  wheel,  extended  from  the 
inlet  opening  to  the  circumference  of  the  wheel. 

Fig.  9  shows  a  vertical  fan  of  this  type.  A  is 
the  movable  disk  which  was  fastened  to  the  shaft 
D,  and  which  carried  the  radial  vanes  B.  The 
fan  was  driven  by  the  pulley  E,  fastened  to  the  shaft 
D.  C  is  the  inlet  duct  leading  to  the  fan.  It 
terminated  at  the  vertical  wall  //,  close  to  which 
the  vanes  B  moved  when  the  fan  was  made  to 
revolve.  The  direction  of  the  flow  of  air  from 
the  inlet  C  through  the  wheel  is  indicated  by  the 
arrows. 

The  disk  A,  with  the  location  of  the  shaft  D, 
and  the  position  and  arrangement  of  the  vanes  B, 
are  shown  in  Fig.  10. 

Figs.   9  and   10  are  taken  from  a -Treatise  on 


32 


CENTRIFUGAL    FANS. 


Ventilation,  by  Wyman,  published  at   Boston  in 
1846. 

It  will  be  noticed  that  this  fan  has  no  casing 
or  housing,  and  that  since  the  vanes  are  radial 


FIG.    9. 

it  will  work  equally  well  whichever  way  it  be 
made  to  revolve.  The  outside  diameter  of  the 
wheel,  measured  to  the  tips  of  the  vanes,  is  about 
twice  the  diameter  of  the  inlet;  and  the  width 


FIRST   TYPE    OF    FANS.  33 

of  the  vanes,  measured  from  the  inlet  to  the  disk 
A  is  about  one-half  the  diameter  of  the  inlet,  or 
one-quarter  the  diameter  of  the  wheel. 

The  vanes  B  were  made  to  revolve  as  close  to 
the  face  of  the  wall  H  as  possible  in  order  that 


FIG.  10. 

the  leakage  through  the  space  between  the  vanes 
and  the  wall  should  be  small. 

Figs.  11  and  12  show  an  early  form  of  a  wheel 
of  this  type  with  vanes  as  recommended  by 
Combes.  This  form  of  wheel  is  shown  by  Delaunay 
in  his  Cours  Elementaire  de  Mecanique,  published 
at  Paris  in  1854. 

In  the  figures,  A  is  the  moving  disk  to  which 


34 


CENTRIFUGAL    FANS. 


the  vanes  D  were  fastened,  and  which  was  mounted 
on  the  shaft  B.  C  is  the  pulley,  which  was  mount- 
ed on  the  shaft  B,  by  which  the  fan  was  driven 


FIG.  11. 


This  fan,  like  the  one  shown  in  Figs.  9  and  10, 
had  only  one  movable  disk,  and  it  was  placed  close 
to  a  vertical  wall  H  through  which  the  inlet  duct 


FIRST   TYPE   OF    FANS.  35 

E  passed.  The  air  flowed  from  the  inlet  duct  E 
through  the  fan  and  was  discharged  at  all  parts 
of  the  circumference. 

The  diameter  of  the  inlet  of  the  wheel  was 
about  0.7  the  diameter  of  the  wheel,  and  the 
width  of  the  wheel  was  about  one-half  the  diam- 


FIG.  12. 

eter  of  the  inlet.  The  vanes  were  very  much 
curved,  and  the  wheel  was  run  with  the  convex 
part  of  the  vanes  forward,  as  indicated  by  the 
arrow  in  Fig.  12. 

Tests  made  with  some  of  the  earlier  types  of 
wheels   with    vanes    curved    as    recommended   by 


36  CENTRIFUGAL    FANS. 

Combes  show  that  vanes  with  much  curvature 
were  not  so  efficient  as  straighter  vanes.  It  seems 
that  they  were  not  so  effective  in  imparting  a 
motion  of  rotation  to  the  air  as  were  the  straighter 
and  more  nearly  radial  vanes. 

The  later  fans  of  this  type,  most  of  which  had 
two  moving  disks  with  the  vanes  between,  re- 
sembled very  much  the  modern  fans  of  that  type 
known  as  the  <4  cone  wheel." 

The  Second  or  Guibal  Type  of  Fans.  The  pe- 
culiarity of  the  fans  of  this  type  is  that  they  always 
had  casings  or  housing  in  which  the  wheel  carrying 
the  vanes  revolved.  These  housings  were  always 
fitted  close  to  the  wheels  and  had  either  one  or 
two  openings  at  the  center  through  which  the  air 
entered.  When  there  were  two  openings,  there 
was  one  on  ench  side  of  the  housing.  The  air  was 
discharged  from  only  one  part  of  the  periphery  of* 
the  wheel  instead  of  from  every  part  as  in  the 
first  type  of  fans. 

Fig.  13  shows  a  sectional  view  of  a  Guibal  fan 
taken  from  an  illustration  given  in  Chauffage  et 
Ventilation,  by  Planat.  A  is  the  inlet;  B,  the 
vanes ;  C,  the  housing  or  casing ;  D,  the  outlet  flue ; 
and  E,  a  movable  screen  which  could  be  moved 
up  or  down  in  the  groove  F,  thus  increasing  or 
diminishing  the  area  of  the  outlet  opening  //, 
through  which  the  air  escaped  from  between  the 
blades  or  vanes  of  the  wheel  into  the  outlet  flue  D. 


SECOND    TYPE    OF   FANS. 


37 


It  will  be  noticed  that  the  housing  is  fitted 
close  to  the  wheel,  and  that  air  can  escape  from 
the  wheel  only  when  one  of  the  spaces  between 
two  consecutive  vanes  is  opposite  the  opening  H. 
It  was  found  as  the  result  of  experience  and  ex- 
periments that  for  every  fan  there  was  a  par- 
ticular area  of  the  opening  H  which  gave  the 


FIG.  13. 

greatest  calculated  efficiency.  And  as  it  was 
impossible  to  calculate  this  best  area  of  the  open- 
ing H ,  the  screen  E  was  made  so  as  to  be  adjust- 
able in  the  groove  F. 

The  vanes  are  shown  flat  and  bent  forward 
at  the  outer  tips;  and  at  the  inlet  end  they  are 
inclined  backward  at  an  angle  or  about  45°  with 
the  radius.  The  vanes  were  often  put  in  so  as  to 


38  CENTRIFUGAL    FANS. 

coincide  with  the  radius,  and  at  other  times  they 
were  curved.  For  fans  of  this  type  there  was  never 
a  moving  disk  to  which  the  vanes  were  fastened 
and  which  moved  with  them.  The  sides  of  the 
housing  took  the  place  of  the  disks  of  the  earlier 
type  of  fans,  and  these  sides  were  always  station- 
ary and  made  to  fit  close  to  the  wheels. 

The  diameter  of  the  inlet  of  the  fan  shown  in 
Fig.  13  is  seen  to  be  less  than  half  the  diameter  of 
the  wheel,  and  it  is  probable  that  there  were  two 
inlets,  one  in  each  side  of  the  housing.  As  these 
fans  could  be  used  either  as  exhausters  or  blowers, 
they  were  placed  either  at  the  top  of  the  air-shaft 
of  the  mine  to  be  ventilated  or  at  the  bottom, 
depending  upon  which  was  the  more  convenient 
in  each  particular  case. 

Planat  does  not  say  how  wide  the  particular 
fan  shown  in  Fig.  13  was,  although  it  is  probable 
that,  judging  from  other  fans  of  the  same  type, 
the  width  was  equal  to  about  one-half  the  diam- 
eter of  the  inlet. 

The  outlet  flue  D  is  shown  tapering,  with  the 
small  end  at  the  bottom.  Some  of  the  earlier 
Guibal  fans  were  put  up  with  square  outlet  flues, 
but  Guibal  conceived  the  idea  of  gradually  re- 
ducing the  velocity  of  the  air  as  it  passed  up  the 
flue  from  the  fan  to  the  flue  outlet,  in  order  to 
avoid  the  loss  of  head  due  to  a  sudden  decrease 
in  velocity.  The  result  was  that  most  of  the 
Guibal  fans  of  which  one  finds  descriptions,  have  the 


THIRD    TYPE    OF    FANS.  39 

tapering  outlet  flue  mentioned  in  connection  with 
them.  In  fact,  this  tapering  outlet  flue  with  the 
small  end  at  the  fan  outlet  is  often  mentioned  as 
one  of  the  characteristics  of  a  Guibal  fan  installa- 
tion. 

The  Third  Type  of  Fans.  This  type  of  fans 
resembles  very  much  the  second  or  Guibal  type. 
It  had  always  a  casing  to  the  fan  wheel,  but  the 
casing  differed  from  that  of  the  Guibal  type  of 
fans  in  that  it  was  what  was  known  to  the  earlier 
writers  as  an  eccentric  casing.  The  casing  really 
consisted  of  a  scroll  which  was  close  to  the  wheel 
at  one  point  and  gradually  left  the  wheel  so  that 
it  surrounded  the  wheel  in  the  form  of  a  spiral. 
The  writer  has  been  unable  to  determine  whether 
this  type  of  fan  is  earlier  than  the  Guibal  type 
or  whether  it  is  later.  It  is  extremely  difficult  to 
get  exact  dates  as  to  the  introduction  of  the 
closed  or  encased  type  of  fans,  and  it  is  espe- 
cially difficult  to  determine  whether  the  fan  with 
the  closely  fitted  casing  antedated  the  fan  with  the 
spiral  or  eccentric  casing. 

Fig.  14  shows  a  fan  of  this  type  which  is  repro- 
duced from  an  illustration  in  lire's  Mechanical 
Dictionary  of  Arts,  Manufacturers  and  Mines, 
published  in  New  York,  in  1844,  from  the  third 
London  edition. 

It  will  be  noticed  that  this  fan  shows  a  casing 
in  the  form  of  a  scroll  or  spiral,  but  Ure  in  his 


40 


CENTRIFUGAL    FANS. 


description  does  not  say  whether  or  not  it  is  a 
true  scroll  or  spiral.  Later  drawings  of  wheels 
of  this  type  show  the  casing  as  a  true  spiral, 
and  later  writers  in  speaking  of  the  casing  say 
that  the  scroll  should  be  of  the  form  of  an  Archi- 
medean spiral.  Some  drawings  show  the  casing 


FIG.   14. 

as  circular  but  of  larger  diameter  than  the  wheel 
and  eccentric  to  it  instead  of  concentric,  and 
hence  fans  of  this  type  were  often  called  "  eccen- 
tric" fans,  to  distinguish  them  from  the  fans  of 
the  Guibal  type  which  had  circular  casings  that 
were  close  fitting  to  the  wheel. 


THIRD    TYPE    OF     FANS.  41 

The  object  of  the  scroll  or  spiral  casing  was 
to  enable  air  to  be  discharged  from  all  points  of 
the  periphery  of  the  wheel,  and  there  should  be 
therefore  a  gradual  increase  of  the  distance  be- 
tween the  spiral  and  the  circumference  of  the 
wheel  from  the  point  at  which  the  spiral  is  nearest 
the  wheel  to  the  opening  of  the  discharge.  When 
the  scroll  or  spiral  was  of  the  proper  proportions 
there  was  an  almost  uniform  discharge  from  all 
parts  of  the  periphery  and,  therefore,  an  almost 
uniform  inward  flow  at  the  entrance  and  through 
the  wheel  between  the  vanes.  In  the  fans  of  the 
Guibal  type  there  was  no  flow  except  through  the 
space  between  two  consecutive  vanes  which  were 
opposite  the  outlet  opening,  and  as  soon  as  this 
space  was  moved  away  from  the  outlet  opening 
the  flow  through  it  ceased,  but  began  through  the 
space  between  two  other  vanes.  There  was, 
therefore,  an  intermittent  flow  through  the  space 
between  each  pair  of  vanes,  and  the  starting  and 
stopping  of  the  flow  through  the  spaces  between 
the  vanes  made  the  fans  less  efficient  than  fans 
where  the  flow  through  the  wheel  was  continuous 
and  uniform  at  all  times  for  the  same  speed  of 
the  wheel. 

Fig.  15  shows  diagrammatically  the  form  of 
spiral  which  was  used  on  the  latter  fans  of  this 
type.  A  is  the  entrance  and  B  the  outlet.  The- 
scroll  began  at  the  point  a  where  it  was  quite  close 
to  the  wheel,  and  ended  at  the  point  e.  The 


42 


CENTRIFUGAL   FANS. 


wheel  was  supposed  to  revolve  as  indicated  by 
the  arrow.  Following  the  scroll  from  the  be- 
ginning to  the  end,  in  the  direction  of  the  motion 
of  the  wheel,  the  space  between  the  wheel  and 
the  scroll  gradually  and  uniformly  increased.  If 


FIG.   15. 

the  space  between  the  points  a  and  e,  the  first 
and  last  points  of  the  scroll,  was  s;  the  space 
between  the  wheel  and  scroll  at  6,  one-quarter  the 

circumference  of  the  wheel  from  a,  would  be  —  ; 
at  c,  one-half  the  circumference  from  a,  the  space 


THIRD   TYPE    OF    FANS.  43 

between  the  wheel  and  the  scroll  would  be  -7- ;  and 

at  d,  the  space  would  be  - 

A  curve  such  as  shown  in  Fig.  15,  drawn  about 
a  circle  in  such  a  way  that  the  distance  between 
the  curve  and  the  circumference  increases  directly 
as  the  distance  measured  on  the  circumference  of 
the  circle,  from  the  starting  point,  is  an  Archi- 
medean spiral.  This  is  the  curve  which  was  sup- 
posed to  be  used  with  fans  of  this  type.  Ordi- 
narily, however,  the  true,  exact,  Archimedean 
spiral  was  not  used,  but  approximations  made  up 
of  arcs  of  circles  were  used.  If  the  curve  was 
made  up  of  parts  or  arcs  of  two  circles  it  was 
called  a  "  two  radius  "  scroll  or  spiral;  if  made 
up  of  three  arcs  it  was  called  a  "  three  radius  " 
spiral;  if  of  four  arcs,  a  "four  radius"  spiral, 
etc. 

Fans  of  this  type  were  usually  small  as  com- 
pared to  fans  of  the  preceding  types  and  the 
wheels  were  run  at  a  considerable  number  of  revo- 
lutions per  minute,  so  that  the  air  was  given 
the  same  velocity  of  rotation  by  means  of  the 
smaller  wheels  running  at  a  high  speed  as  it 
would  be  by  means  of  the  larger  wheels  running 
at  a  comparatively  low  number  of  revolutions. 
The  width  of  the  wheel  in  the  earlier  fans  of  this 
type  was  usually  uniform  from  the  center  to  the 
periphery;  in  the  later  forms,  however,  the  width 


44  CENTRIFUGAL    FANS. 

at  the  periphery  was  less  than  that  at  the  center 
in  almost  the  same  proportion  as  that  found  in 
modern  wheels. 

When  fans  of  this  type  were  made  with  a 
double  entrance,  that  is  to  say  when  there  was 
an  inlet  opening  in  each  side  of  the  casing  for  the 
entrance  of  the  air,  the  wheels  were  often  pro- 
vided with  a  central  disk  to  which  the  vanes  or 
paddles  of  the  fans  were  attached  and  which  really 
made  of  the  double  admission  fan,  two  single 
admission  fans  joined  together. 

Modern  Type.  Fans  of  the  modern  type  may  be 
divided  into  two  classes.  One  is  an  improvement 
on  and  in  every  way  similar  to  the  third  type  of 
fans  described  before.  This  class  includes  all  of 
the  ordinary  centrifugal  blowers  and  exhausters. 
The  other  class  of  modern  fans  includes  what  are 
known  as  "  cone  wheels,"  and  is  an  improvement 
on  the  first  type  of  fans. 

The  ordinary  centrifugal  blower  or  exhauster 
consists  of  a  wheel  carried  on  a  shaft  which  re- 
volves inside  of  a  casing  or  as  it  is  commonly 
called,  a  "housing."  The  housing  is  always  in 
the  shape  of  a  spiral  about  the  wheel  and  has 
either  one  or  two  inlets  for  the  air.  If  there  are 
two  inlets,  one  in  each  side  of  the  housing, 
the  fan  is  called  a  "  doable  admission  fan,"  and 
if  there  is  but  one  entrance  or  inlet  for  the  air 
the  fan  is  called  a  "  single  admission  fan."  In 


MODERN  TYPE   OF    FANS.  45 

order  that  there  may  be  as  little  impediment  as 
possible  to  the  flow  of  air  into  the  fan  during 
operation  the  single  admission  fans  are  often 
made  so  that  both  of  the  bearings  for  the  shaft 
of  the  wheel  are  on  the  same  side  of  the  housing, 
and  then  the  wheel  is  said  to  be  overhung.  In 
double  admission  fans  it  is  impossible  to  avoid 
having  the  bearings  in  front  of  one  of  the  inlets 
so  there  is  usually  a  bearing  on  each  side  of  the 
housing.  The  result  of  this  is  that  the  area  of 
the  inlets  in  a  double  admission  fan  is  usually 
considerably  reduced  by  the  space  occupied  by 
the  shaft  and  the  bearings,  and  as  the  fans  are  usu- 
ally driven  by  a  pulley  fastened  to  the  shaft  this 
pulley  by  obstructing  one  of  the  inlets  interferes 
with  the  entrance  of  the  air  through  that  par- 
ticular inlet  to  a  very  considerable  degree.  If 
the  fan  be  driven  by  a  direct  attached  motor  or 
engine  instead  of  a  pulley  there  is  then  a  still 
greater  obstruction  to  the  entrance  of  the  air 
through  one  of  the  inlets.  The  result  is  that  a 
double  admission  fan  has  its  inlets  so  obstructed 
that  it  is  little  better  than  a  single  admission  fan 
with  an  overhung  wheel.  Exhausters  are  always 
made  with  a  single  inlet,  while  blowers  are  made 
with  either  a  single  or  a  double  inlet. 

In  the  trade,  fans  are  usually  designated  ac- 
cording to  the  shape  of  the  housing;  the  number 
of  inlets ;  the  location  of  the  outlet ;  and  the  direc- 
tion of  the  flow  of  the  air  when  leaving  the  outlet. 


46 


CENTRIFUGAL    FANS. 


Fig.  16  shows  a  side  view  of  what  is  known  as  a 
full  housed,  double  admission,  horizontal,  top  dis- 
charge fan;  and  Fig.  17  shows  a  section,  in  the 
direction  of  the  axis  of  the  wheel,  of  the  same 
fan.  This  fan  is  called  a  "  full  housed  "  fan  be- 
cause all  the  casing  or  housing  is  shown  above 


FIG.  16. 


the  foundation  on  which  the  fan  rests.  If  a  part 
of  the  housing  or  casing  of  the  fan  projects  below 
the  foundation  so  that  the  wheel  revolves  in  a 
pit  as  shown  in  Fig.  18  the  fan  is  called  a  "  three- 
quarter  housed  "  fan.  It  is  evident,  of  course, 


47 


FIG.   17. 


48 


CENTRIFUGAL    FANS. 


that  in  the  case  of  a  three-quarter  housed  fan  all 
of  the  inlet  or  entrance  opening  must  be  above 
the  foundation  in  order  to  give  free  admission  to 
the  air. 

If  the  outlet  of  the  fan  is  at  the  top  of  the 
housing  and  the  air  is  blown  in  a  horizontal  di- 
rection as  shown  in  Fig.  15,  the  fan  is  called  a 


FIG.  18. 

"  top,  horizontal  discharge  "  fan.  If,  however, 
the  outlet  of  the  fan  is  at  the  top  and  the  air  is 
blown  upward  instead  of  horizontally,  the  fan  is 
called  a  "  top,  up  discharge  "  fan.  If  the  outlet 
is  at  the  bottom  and  the  air  is  blown  horizontally 
the  fan  is  called  a  "  bottom,  horizontal  discharge  " 
fan. 

The  fan  in  Fig.  18  has  a  single  inlet,  the  outlet 


MODERN   TYPE  OF    FANS. 


49 


is  at  the  top  and  the  air  is  discharged  upward;  it 
is  called,  therefore,  a  "  three-quarter  housed, 
single  admission,  top,  up  discharge  "  fan. 

Fans  are  sometimes  made  with  two  outlets  as 
shown  in  Fig.  19,  where  the  air  is  discharged  from 


FIG.  19. 

the  housing  at  the  top  towards  the  right  and  at 
the  bottom  towards  the  left.  Such  fans  are  known 
as  "  double  discharge  "  fans,  and  they  are  made 
so  that  the  same  or  different  quantities  of  air  pass 
out  through  each  outlet. 

The  ordinary  commercial  fan  used  for  heating 


50  CENTRIFUGAL   FANS. 

and  ventilating  work  or  for  mechanical  draft  has 
the  housing  made  of  sheet  steel  put  together  with 
angle  irons,  and  well  braced  on  the  outside  with 
angle  irons  so  as  to  enable  it  to  withstand  the 
pressure  and  racking  due  to  the  movement  of  the 
wheel.  The  part  that  rests  on  the  foundation  is 
usually  reinforced  by  heavy  angle  irons  varying 
in  size  from  the  ordinary  commercial  3x3  angle 
to  the  6x6  angle.  In  some  cases  where  very  large 
wheels  are  used  for  ventilating  work  the  housing 
is  built  up  of  wood  and  brick. 

The  housings  and  the  shapes  and  dimensions 
of  the  scrolls  or  spirals  will  be  discussed  in  a 
later  chapter.  It  suffices  to  say  here  that  the 
scrolls  are  usually  either  three  or  four  radius 
scrolls '  or  spirals. 

The  type  of  centrifugal  fan  that  is  used  nowa- 
days and  known  as  a  cone  wheel  is  very  similar 
indeed  to  the  early  fans  described  under  the  first 
type.  It  is  seldom  used  where  air  is  to  be  discharged 
against  any  considerable  pressure  but  is  very 
largely  used  for  heating  and  ventilating  work 
where  the  air  is  to  be  moved  against  little  pressure 
and  where  the  object  is  to  move  a  large  quantity 
of  air  against  a  low  pressure.  This  fan  will  be 
discussed  later. 


CHAPTER  IV. 


Fan  Wheel.  A  fan  wheel  of  the  ordinary  type 
used  for  heating  and  ventilating  work  is  shown 
in  perspective  in  Fig.  20.  A  represents  the  side 
plates  between  which  are  fastened  the  blades 
5,  commonly  called  vanes  or  "  floats."  To  these 
vanes  are  riveted  tee  irons  C  which  are  cast  into 
the  hub  of  the  wheel.  One  set  of  these  tee  irons 
constitutes  what  is  called  a  "  spider."  It  will  be 
noticed  that  in  Fig.  20  there  are  two  sets,  one  near 
each  side  of  the  wheel.  Such  a  wheel  is  said  to 
have  a  double  spider.  Small  wheels  4  feet  or  less 
in  diameter  usually  have  a  single  spider. 

The  side  plates  A  are  usually  reinforced  at  the 
inlet  of  the  wheel  by  a  strip  of  iron  or  an  angle 
iron  as  indicated  by  D  in  the  figure. 

When  the  wheel  is  in  the  housing  supported 
on  the  shaft  which  passes  through  the  hub,  the 
air  enters  through  the  inlet  and  passes  radially 
outward  between  the  side  plates  A  to  the  periphery 


52 


CENTRIFUGAL   FANS. 


of  the  wheel  and  from  there  passes  into  the  hous- 
ing. It  will  be  noticed  that  the  air  is  confined 
between  the  side  plates  A  as  long  as  it  is  passing 


through  the  wheel  and  it  is  thus  made  to  more 
readily  take  up  the  motion  of  rotation  of  the  wheel. 
In  this  respect  the  fans  of  the  modern  type  differ 


VANES    OR    FLOATS.  53 

from  those  of  the  earlier  types.  In  the  earlier 
types  the  blades  were  not  provided  with  the  side 
plates  A  but  they  revolved  directly  between  the 
sides  of  the  casing  or  housing. 

Vanes  or  Floats.  There  does  not  seem  to  be 
any  rule  or  formula  for  determining  the  number 
of  vanes  or  floats  that  a  wheel  should  have.  There 
should  be  enough  to  insure  that  the  air  passing 
from  the  wheel  will  be  given  the  same  velocity  of 
rotation  that  the  wheel  has  before  it  leaves  the 
periphery,  but  there  should  not  be  so  many  as  to 
make  the  space  between  two  consecutive  floats  so 
narrow  as  to  offer  undue  friction  to  the  flow  of  the 
air  from  the  center  towards  the  periphery  of  the 
wheel.  According  to  the  old  rule  which  was 
sometimes  used  there  should  be  one  float  for  every 
foot  in  diameter  of  the  wheel.  This  meant  that 
at  the  periphery  of  the  wheel  the  floats  would  be 
about  37|  inches  apart.  That  rule  does  not.  hold 
good  with  modern  fans,  as  even  the  smaller  sizes, 
2^  or  3  feet  in  diameter,  usually  have  6  floats,  and 
the  larger  wheels  seldom  have  more  than  12  floats. 
Different  manufacturers  have  different  ideas 
about  curving  the  floats.  Some  seem  to  think 
that  they  should  extend  from  the  center  towards 
the  periphery  of  the  wheel  in  a  radial  direction  as 
indicated  in  Fig.  21.  Others  give  the  floats  a 
slight  bend  or  curve  at  the  outer  end  near  the 
periphery  of  the  wheel  as  shown  in  Fig.  22,  in 


54  CENTRIFUGAL    FANS. 

order,  as  they  claim,  to  decrease  the  noise  made 
when  the  wheel  is  working  in  the  housing.  Still 
others  give  the  floats  a  considerable  curve  from 
the  entrance  to  the  outer  periphery,  as  shown  in 
Fig.  23.  When  the  floats  are  put  in  radially  it 


FIG.  21. 

makes  no  difference  which  way  the  wheels  revolve, 
but  when  they  are  curved  as  shown  in  Figs.  22 
and  23  the  wheels  should  be  revolved  so  that  the 
convex  part  of  the  float  goes  forward  as  indicated 
by  the  arrows.  When  the  floats  are  curved  as 
indicated  in  Fig.  23  and  this  curvature  is  very 
pronounced,  it  is  found  that  the  wheel  will  not  work 


VANES    OR    FLOATS.  55 

as   well   against  a  high  pressure  as  a  wheel  with 
straighter  and  more  nearly  radial  floats. 

It  will  be  noticed  that  the  curved  floats  shown 
in  Fig.  22  are  tangent  to  the  radius  at  the  inlet. 
This  is  the  way  in  which  all  the  fan  makers  who 
use  curved  floats  put  them  in.  This  is  rather 


FIG.  22. 

curious  in  the  face  of  the  fact  that  theoretical  de- 
ductions indicate  that  the  floats  should  be  tangent 
to  the  radius  at  the  periphery  of  the  wheel  and 
that  at  the  inlet  they  should  make  an  angle  of 
about  45°  with  the  radius.  Most  writers  who 
have  attempted  to  discuss  the  theory  of  fans  have 


56  CENTRIFUGAL    FAXS. 

urged  this  point,  and  it  seems  to  the  author  that 
it  is  well  taken  because  the  velocity  of  the  air  in 
the  direction  of  the  radius  of  the  wheel  is  usually 
about  equal  to  the  velocity  of  rotation  of  the 
edges  of  the  floats  at  the  entrance,  and  hence  the 


FIG.  23. 

air  would  enter  the  space  between  the  floats  with 
less  shock  and  probably  with  less  loss  of  head  if 
the  floats  were  inclined  at  the  entrance  to  an  angle 
of  about  45°  with  the  radius.  In  order  that  the 
air  may  be  given  as  nearly  as  possible  the  same 
velocity  of  rotation  that  the  floats  have,  they 
should  be  radial  at  the  outer  end  near  the  periph- 


VANES    OR    FLOATS. 


57 


ery,  and  when  working  against  a  pressure  it  is 
absolutely  necessary  that  the  floats  be  radial  at 
the  outer  periphery  of  the  wheel;  hence,  it  seems 
that  the  floats  should  be  curved  as  indicated  in 
Fig.  24.  Wheels  with  floats  curved  as  indicated 
in  Fig.  24  are  illustrated  in  Ventilationsmaschinen 


FIG.  24. 


der  Bergwerke  by  von  Hauer,  published  at  Leipsic, 
1870.  As  far  as  the  author  knows,  however,  no 
modern  fans  have  been  made  with  blades  curved 
as  indicated  in  Fig.  24  nor  are  there  any  recorded 
tests  of  the  fans  of  this  type  as  shown  by  von 
Hauer, 


58 


CENTRIFUGAL   FANS. 


The  shape  of  the  floats  is  shown  in  Figs.  25 
and  26,  where  A  represents  the  side  plates;  B,  the 
float;  C,  tee  irons  of  the  spider;  E,  the  heel  or  inner 
part  of  the  float;  and  F,  the  tip  or  outer  part 


of  the  float.  It  will  be  noticed  that  the  heel  ex- 
tends somewhat  below  the  side  plates  A  and  as 
the  side  plates  extend  from  the  inlet  to  the  cir- 
cumference of  the  wheel  the  heel  of  the  float  ex- 


VANES    OR    FLOATS. 


59 


tends  below  the  inlet.  The  heel  of  the  float  is 
usually  at  a  distance  from  the  center  of  the  wheel 
equal  to  one-quarter  the  diameter  or  one-half  the 
radius  of  the  wheel.  The  object  of  extending  the 
floats  towards  the  center  is  to  set  in  motion  the 
air  between  the  circumference  of  the  inlet  and 


the  center  of  the  wheel,  and  thus  make  it  easier 
for  the  wheel  to  give  the  air  during  its  passage 
through  the  wheel  the  same  velocity  of  rotation  that 
the  floats  have.  The  floats  shown  in  Fig.  25  are 


60  CENTRIFUGAL    FANS. 

for  a  wheel  with  a  double  spider,  and  the  floats 
shown  in  Fig.  26  are  for  a  wheel  with  a  single  spider. 
Inlet.  In  the  earlier  types  of  fans  the  diameter 
of  the  inlet  was  almost  alwrays  made  equal  to  one- 
half  the  diameter  of  the  wheel,  but  in  the  modern 
fans  the  diameter  of  the  inlet  is  proportioned 
according  to  the  use  to  which  the  fan  is  to  be  put. 
If  the  fan  is  to  work  against  comparatively  low 
pressures  and  is  intended  primarily  for  moving  a 
large  amount  of  air  the  diameter  of  the  inlet  is 
larger  than  it  would  be  if  the  fan  were  intended 
primarily  for  moving  small  quantities  of  air 
against  a  considerable  pressure.  The  ratio  of  the 
diameter  of  the  inlet  to  the  diameter  of  the  wheel 
is  usually  designated  by  the  letter  r  so  that  in 
Figs.  25  and  26  where  D  is  used  to  indicate  the 
diameter  of  the  wheel,  the  diameter  of  the  inlet 
is  indicated  by  D  r.  In  most  fans  used  for  heating 
and  ventilating  work  it  will  be  found  that  r  is 
either  f,  equal  0.625;  or  ^/2t  equal  0.707.  But 
for  fans  used  to  work  against  a  considerable  pres- 
sure, several  ounces  per  square  inch,  r  will  often 
be  0.5  or  even  less.  If  r  be  made  much  greater 
than  0.7  it  will  be  found  that  the  wheel  cannot 
move  the  air  against  a  pressure,  because  the  dis- 
tance which  the  air  travels  in  passing  radially 
through  the  wheel  is  so  short  that  it  does  not 
have  time  to  acquire  the  velocity  of  rotation  of 
the  floats. 


WIDTH.  61 

Width.  In  the  earlier  types  of  fans  the  width, 
W,  of  the  fan  and  therefore  the  width  of  the 
wheel  was  always  made  such  that  the  area  for  the 
radial  flow  of  air  through  the  wheel  at  the  en- 
trance was  equal  to  the  area  of  the  entrance. 
Sometimes,  of  course,  in  order  to  allow  for  fric- 
tion the  area  for  the  radial  flow  of  air  through  the 
wheel  was  made  slightly  larger  than  the  area  of 
the  entrance.  The  area  for  the  radial  flow  of  the 
air  through  the  wheel  at  the  entrance  is  equal  to 
the  area  of  the  surface  of  a  cylinder  whose  base  is 
the  diameter  of  the  inlet  and  whose  height  is  the 
width  of  the  wheel.  The  area  of  the  surface  of 
such  a  cylinder  is  equal  to  n  r  D  W ;  and  the  area 
of  the  inlet,  assuming  that  there  is  only  one  inlet, 

n  r2  D2 

is   equal     to  In   order  that  these    two 

4 

areas  may  be  equal  to  one  another  it  is  evident 
that  W,  the  width  of  the  fan,  must  be  equal  to 
one-quarter  the  diameter  of  the  inlet.  If  the  fan 
is  a  double  admission  fan  and  has  two  inlets,  then 
the  width  of  the  fan  must  be  at  least  one-half  the 
diameter  of  the  inlet,  or  double  what  it  should  be 
for  a  single  admission  fan. 

Most  fans  used  for  heating  and  ventilating  work 
are  made  -with  the  width  equal  to  one-half  the 
diameter  of  the  wheel,  and  this  is  the  width  of 
what  is  called  a  standard  fan.  What  is  known 
as  a  narrow  fan  is  one  for  which  the  width  is  three- 
eighths  the  diameter  of  the  wheel. 


62  CENTRIFUGAL   FANS. 

The  width  of  the  fan  does  not  affect  the  quan- 
tity of  air  which  it  can  handle  per  minute,  or  the 
pressure  against  which  the  air  can  be  forced,  so 
long  as  it  is  not  less  than  one-quarter  the  diameter 
of  the  inlet  for  a  single  admission  fan  and  one-half 
the  diameter  of  the  inlet  for  a  double  admission 
fan. 

In  modern  fans  the  floats  are  made  to  narrow 
from  the  entrance  to  the  periphery  of  the  wheel 
in  such  a  way  as  to  make  the  radial  velocity  of  the 
air  passing  through  the  wheel  nearly  uniform  from 
the  entrance  to  the  periphery.  The  width  at  the 
periphery  is  usually  about  25  per  cent,  greater 
than  would  be  theoretically  necessary  in  order 
that  the  radial  velocity  of  the  air  through  the 
wheel  should  be  uniform  from  the  inlet  to  the 
periphery  of  the  wheel.  The  area  through  which 
the  air  passes  radially  at  the  inlet  is  K  r  D  W ; 
and  calling  w  the  width  of  the  float  at  the  periph- 
ery the  area  through  which  the  air  passes  radially 
at  the  periphery  of  the  wheel  is  TL  D  w.  In  order 
that  these  two  expressions  may  be  equal  to  one 
another  it  is  evident  that 

(12)  w  =  r  W 

From  this  it  is  seen  that  the  width  at  the  periph- 
ery bears  the  same  ratio  to  the  width  at  the  en- 
trance that  the  diameter  of  the  inlet  bears  to  the 
diameter  of  the  wheel. 


WIDTH.  6.3 

As  said  before,  it  is  usual  to  make  the  width  at 
the  periphery  25  per  cent,  greater  than  would  be 
necessary  in  order  that  the  velocity  of  the  air 
in  the  direction  of  the  radius  of  the  wheel  should 
be  uniform  from  the  inlet  to  the  periphery,  and 
hence  the  width  at  the  periphery  is  usually 


CHAPTER  V. 


Capacity.  The  capacity  of  a  fan  means  the 
maximum  number  of  cubic  feet  of  air  discharged 
by  it  per  minute  against  a  pressure  corresponding 
to  the  velocity  of  the  tips  of  the  floats  of  the 
wheel. 

As  has  been  pointed  out  when  discussing 
vortexes,  the  pressure  in  the  housing  of  a  fan 
will  be  that  corresponding  to  the  velocity  of  the 
tips  of  the  floats,  when  the  velocity  in  the  direc- 
tion of  the  radius  at  entrance  is  less  than  or  equal 
to  the  velocity  of  rotation  of  the  parts  of  the 
floats  at  the  entrance.  If  the  velocity  of  the 
air  through  the  inlet  be  greater  than  the  radial 
velocity  at  the  inlet,  the  difference  between  the 
heads  corresponding  to  these  two  velocities  is 
lost.  Hence  the  only  advantage  of  making  the 
wheels  wider  than  necessary  to  make  the  radial 
velocity  at  the  inlet  equal  to  the  velocity  through 
the  inlet,  is  that  the  air  will  be  longer  in  the 

64 


CAPACITY.  65 

wheel  and,  therefore,  be  more  likely  to  acquire 
the  same  velocity  of  rotation  as  the  floats. 

In  order  that  the  pressure  in  the  housing  shall 
be  equal  to  that  corresponding  to  the  velocity  of 
the  tips  of  the  floats,  neither  the  velocity  through 
the  inlet  nor  the  radial  velocity  at  the  inlet  must 
be  greater  than  the  velocity  of  rotation  of  the 
points  of  the  floats  at  the  inlet. 

Hence  the  maximum  number  of  cubic  feet  of 
air  discharged  by  a  fan  against  a  pressure  cor- 
responding to  the  velocity  of  the  tips  of  the  floats 
is  equal  to  the  product  of  the  velocity  of  the 
parts  of  the  float  at  the  inlet  multiplied  by  the 
area  of  the  inlet,  or  by  the  area  through  which 
the  air  passes  radially  at  the  inlet  if  it  be  smaller 
than  the  area  of  the  inlet. 

Let  us  assume  that  we  have  a  single  admission 
fan,  the  diameter  of  whose  wheel  in  feet  is  D.  Then 
the  diameter  of  the  inlet  will  be  r  D,  as  explained 

before,    and   the   area  of   the  inlet  will  be  — *—. — . 

4 

This  we  will  assume  is  less  than  the  area  through 
which  the  air  passes  readily  at  the  inlet,  as  it  will 
be  if  the  width  of  the  fan  is  greater  than  one- 
quarter  the  diameter  of  the  inlet. 

The  velocity  per  minute  of  the  points  of  the 
floats  at  the  inlet  will  be  n  r  D  N,  where  N  is  the 
number  of  revolutions  made  per  minute  by  the 
wheel. 

And  if,  as  explained  in  previous  articles,  we 


66  CENTRIFUGAL    FANS. 

call  c  the  coefficient  of  discharge,  we  have  that 
the  quantity  of  air  C,  in  cubic  feet  entering  the  fan 
per  minute  is 

(14)  C  _<*  +  »* 


The  value  of  c  depends  upon  the  shape  of  the 
inlet  and  is  probably  between  0.50  and  0.62,  and 
may,  therefore,  be  taken  as  0.56. 

The  value  of  n  is  3,1416,  and  hence 


is  equal  to  1.38,  and  (14)  becomes 

(15)  C  =  l.38r*D*N 

Since  the  same  quantity  of  air  must  leave  the 
fan  that  enters  it,  equation  (15)  gives  the  capacity 
or  number  of  cubic  feet  of  air  that  will  be  delivered 
per  minute  by  a  fan  when  the  pressure  in  the 
housing  is  that  corresponding  to  the  velocity  of 
the  tips  of  the  floats  of  the  wheel. 

The  velocity  per  minute  of  the  tips  of  the 
floats  is  T:  D  N,  and  from  (3)  we  have,  calling  P 
the  pressure  in  ounces  per  square  inch  corre- 
sponding to  this  velocity. 

(16)  xDN  =  5200  V^F 
From  (16)  we  have 

(17)  D  N  =  1650  v'77 


CAPACITY.  67 

If  now  we  substitute  in  (15)  for  D  N  its  value 
as  given  by  (17)  we  get 

(18)  C  -  1.38  r5  D2  1650 

=  2280  r3  D2 


As  has  been  said  before,  one  common  value 
of  r  is  f  or  0.625,  and  another  common  value  is 
\/0.5  or  0.707.  Hence  r3  is  usually  either  the 
cube  of  0.625  or  the  cube  of  0.707;  that  is,  r3  is 
either  0.244  or  0.353.  Putting  these  values  of  r3 
in  (18)  we  have 


(19) 


C  =  556  D2  v/p     when  r  =  f  or  0.625 ; 
C  =  804  D2  VP    when  r  =  ^2  of  0.707. 
For  all  practical  purposes  we  may  say 

f  C  =  550  D2  v/P~  when  r  =  0.625; 
(20) 

I  C  =  800  D2  VP~  when  r  =  0.707. 

The  equations  for '  C  given  in  (20)  may  be 
used  for  double  admission  fans  as  well  as  for 
single  admission  fans,  because  in  the  case  of 
double  admission  fans  one  of  the  inlets  has  a 
pulley  before  it  which  impedes  the  flow  into  the 
fan ;  and  both  inlets  are  more  or  less  obstructed  by 
the  shaft  and  the  bearings  which  are  usually 
placed  in  the  inlets.  The  bearings  and  their  sup- 


68  CENTRIFUGAL    FANS. 

ports  take  up  so  much  of  the  inlet  areas  that  the 
sum  of  the  areas  of  the  two  inlets  in  the  case  of  a 
double  admission  fan  is  very  little  if  any  greater 
than  the  area  of  the  one  inlet  of  the  single  admis- 
sion fan. 

Equation  (20)  applies  to  an  exhauster  as  well 
as  to  a  blower,  the  only  difference  being  that  in 
the  case  of  an  exhauster  p  is  the  vacuum  in  ounces 
per  square  inch  maintained  at  the  inlet  when  the 
pressure  at  the  outlet  is  that  of  the  atmosphere]  while 
in  the  blower  p  is  the  pressure  in  ounces  per  square 
inch  in  the  housing  at  the  outlet  when  the  pres- 
sure at  the  inlet  is  that  of  the  atmosphere. 

By  transposing  (20)  and  solving  for  D  we  get 


0.625; 

•»    uu\j      Y'    f 

(21) 


\ 


800~7 


when  r  =  0.707. 


Equation  (20)  is  to  be  used  when  we  wish  to 
find  the  capacity  or  number  of  cubic  feet  of  air 
per  minute  a  fan  of  a  given  diameter  in  feet  will 
deliver  when  working  against  a  given  pressure  in 
ounces  per  square  inch;  and  equation  (21)  is  to  be 
used  when  we  wish  to  find  the  diameter  of  the 
fan  required  to  deliver  a  given  quantity  of  air  per 
minute  against  a  given  pressure  in  ounces  per 
square  inch. 


CAPACITY.  69 

Equation  (20)  shows  how  important  it  is  to 
take  the  diameter  of  the  inlet  into  account  when 
ordering  a  fan,  and  it  also  explains  why  two  fans 
of  different  makes,  similar  in  almost  every  respect 
except  as  to  the  diameter  of  the  inlet  opening, 
will  give  such  widely  different  results  in  actual 
use,  so  far  as  the  quantities  of  air  delivered  by 
them  are  concerned.  When  we  discuss  the  ques- 
tion of  power  required  to  run  a  fan  and  the  ques- 
tion of  efficiency,  also,  we  shall  see  that  the  fan 
with  a  small  inlet  has  certain  advantages  over  a 
fan  with  a  large  inlet.  And  it  will  depend  en- 
tirely upon  the  service  for  which  the  fan  is  to  be 
used  as  to  whether  the  inlet  should  be  large  or 
small. 

EXAMPLE:  —  Determine  the  number  of  cubic 
feet  of  air  delivered  per  minute  by  a  fan  having  a 
wheel  8  feet  in  diameter  with  an  inlet  68J  inches 
in  diameter,  when  working  against  a  pressure  of 
0.5  ounce. 

Here  the  diameter  of  the  wheel  is  96  inches 
and  the  diameter  of  the  inlet  is  68^-  inches,  so  that 

,  -        ?  -  0.707 


Hence  we  have  from  (20) 

C  =  800  X  82  X  V  0.5 
=  800x64x0.707 
=  36200. 
The  same  fan  with  an  inlet  60  inches  in  diam- 


70  CENTRIFUGAL    PANS. 

eter,  making  r  =  0.625,  would  deliver  only  22600 
cubic  feet  of  air  per  minute. 

EXAMPLE: — Determine  the  diameter  of  fan  re- 
quired to  deliver  12000  cubic  feet  of  air  per  minute 
against  a  pressure  of  0.25  ounce. 

Let  us  assume  first  that  r  will  be  0.625,  then  we 
have  from  (21) 


I    12QQO  12000 

\550V(X25  =^    550x0.5 


=  \/43.6  =  6.6 

Now  let  us  assume  that  r  will  be  0.707,  then 
we  have  from  (21) 


-4, 


12000 


80QV025 

=  v  30  =  5.5,  about. 

The  diameter  of  the  inlet  for  the  fan  6.6  feet 
in  diameter  would  be  0.625x6.6  =  4.13  feet  or 
49.5  inches;  and  the  diameter  of  the  inlet  of  the 
smaller  fan  would  be  0.705x5.5  =  3.89  feet  or 
about  46.5  nches. 

Table  II.  gives  the  capacities,  as  calculated  by 
(20)  for  different  pressures,  of  fans  with  inlets 
whose  diameters  are  0.707  of  the  diameters  of  the 
wheels. 


CAPACITY. 
TABLE  II. 

Capacities  01  centrifugal  fans. 


71 


'o'q 

li 

Pressure  per  square  inch  in  ounces. 

S| 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

i.o 

3 

2280 

3220 

3940 

4550 

5100 

5570 

6020 

6440 

6830 

7200 

3i 

3100 

4380 

5360 

6200 

6930 

7600 

8200 

8760 

9300 

9800 

4 

4050 

5730 

7010 

8100 

9050 

9920 

10700 

11400 

12100 

12800 

4* 

5130 

7250 

8880 

10200 

11500 

1250C 

13600 

14500 

15400 

16200 

5 

6330 

8950 

11000 

12700 

14100 

15500 

16700 

17900 

19000 

20000 

5* 

7650 

10800 

13200 

15300 

17100 

18700 

20200 

21600 

23000 

24200 

6 

9100 

12900 

15800 

18200 

20400 

22300 

24100 

25800 

27300 

28800 

*6* 

10700 

15100 

18500 

21400 

23900 

26200 

28300 

30200 

32100 

33800 

7 

12400 

17500 

21500 

24800 

27700 

30400 

32800 

35000 

37200 

39200 

8 

16200 

22900 

28000 

32400 

36200 

39600 

42800 

45800 

48600 

51200 

9 

20500 

29000 

35400 

41000 

45800 

50200 

54200 

58000 

61500 

64800 

10 

25300 

35800 

43800 

50600 

56500 

62000 

67000 

71500 

75900 

80000 

11 

30C03 

43300 

53000 

61200 

68400 

75000 

81000 

86500 

91700 

96800 

12 

36500 

51600 

63200 

73000 

81500  89300 

96500 

100300 

109000 

115000 

*  This  is  an  odd  size,  not  made  by  all  manufacturers. 

TABLE  HA. 

Capacities  of  centrifugal  fans. 


Diam- 
eter of 
wheel 

Pressure  per  square  inch  in  ounces. 

in  feet. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

3 

1570 

2220 

2710 

3130 

3510 

3830 

41  4C 

4420 

470C 

4950 

3* 

2130 

3010 

06  30 

4260 

4760 

522( 

564t 

603C 

640( 

6740 

4 

2780 

3940 

4830 

5570 

623C 

682( 

736C 

784C 

832( 

8800 

H 

3530 

4980 

6110 

7020 

791C 

860C 

935C 

9970 

1060C 

11100 

5 

4350 

6150 

7560 

8730 

970C 

1070C 

U50C 

1230C 

1310C 

13700 

5i 

5260 

7430 

9070 

10500 

1180C 

1290( 

13900 

14800 

1580C 

1.6600 

6 

6260 

8870 

10900 

12500 

1400C 

1530C 

16600 

17700 

1880C 

19800 

<H 

7360 

10400 

12700 

14700 

1640C 

1800C 

19500 

20800 

2210C 

23200 

7 

8530 

12000 

14800 

17000 

1900C 

2090C 

22500 

24100 

25600 

26900 

8 

11100 

15700 

19300 

22300 

24900 

27200 

29400 

31500 

3340C 

35200 

9 

14100 

19900 

24300 

28200 

31500 

34600 

37300 

39900 

42300 

44600 

10 

17400 

24600 

30200 

34800 

38900 

42600 

46100 

49200 

52200 

55000 

11 

21100 

2980G 

36400 

42100 

47000 

51600 

55700 

59500 

63100 

66600 

12 

25100 

35500 

43500 

50200 

56000 

61400 

66400 

69000 

75000 

79100 

72  CENTRIFUGAL    FANS. 

To  find  from  the  table  the  capacity  or  number 
of  cubic  feet  of  air  a  fan  will  deliver  per  minute 
against  a  given  pressure,  find  the  diameter  of  the 
wheel  in  the  first  column,  headed  "  Diameter  of 
wheel  in  feet,"  and  then  look  to  the  right  to  the 
column  having  at  the  top  the  given  pressure,  and 
the  number  in  this  column  on  the  same  line  as 
the  diameter  of  the  wheel  is  the  capacity  of  the 
fan  at  the  given  pressure.  Thus,  to  find  the 
capacity  of  a  fan  having  a  wheel  5  feet  in  diam- 
eter when  working  against  a  pressure  of  0.4  of  an 
ounce  per  square  inch,  look  along  the  line  on 
which  5  is  in  the  first  column,  and  under  the  col- 
umn having  0.4  at  the  top  is  found  the  number 
12700,  which  is  the  capacity  of  the  fan  under  the ' 
given  conditions. 

The  table  may  also  be  used  to  determine  the 
diameter  of  a  wheel  required  to  deliver  a  given 
quantity  of  air  per  minute  at  a  given  pressure. 
Thus,  to  find  the  diameter  of  a  wheel  which  has 
a  capacity  of  30000  cubic  feet  against  a  pressure 
of  0.5  of  an  ounce  per  square  inch,  look  down  the 
column  headed  0.5  until  30000  is  found,  and  the 
diameter  of  the  wheel  will  be  found  on  the  same 
line  but  in  the  first  column.  In  this  particular  case 
30000  is  not  found  in  the  0.5  oz.  column;  27700  is 
found  opposite  the  7-foot  wheel  and  36200  is 
found  opposite  the  8-foot  wheel.  It  now  becomes 
a  question  of  engineering  as  to  which  wheel  should 
be  used.  If  the  7-foot  wheel  is  used  it  will  have 


CAPACITY.  73 

to  be  speeded  up  so  as  to  give  a  pressure  of  0.6 
of  an  ounce  in  the  housing,  and  at  this  speed  it 
will  deliver  30400  cubic  feet  instead  of  30000.  If 
on  the  contrary,  the  8-foot  wheel  be  used  it  will 
have  to  be  slowed  down  so  as  to  give  a  pressure 
in  the  housing  of  about  0.35  of  an  ounce,  but  this 
pressure  may  not  be  sufficient  to  overcome  the 
friction  of  the  air  after  it  leaves  the  fan.  It 
would  probably  be  better  to  use  the  8-foot  wheel, 
even  if  it  gave  more  air  than  required,  because, 
as  will  be  seen  later,  the  power  required  to  run 
the  8-foot  wheel  and  deliver  30000  cubic  feet  of 
air  per  minute  will  be  less  than  that  required  for 
the  7-foot  wheel. 

Table  HA  gives  the  capacity  of  fans  having 
wheels  with  inlets  whose  diameters  are  0.625  of  the 
diameter  of  the  wheel.  In  every  other  respect  it 
is  exactly  like  Table  II. 

EXAMPLE: — Determine  the  capacity  of  a  fan 
with  a  5-foot  wheel,  whose  inlet  is  37.5  inches  in 
diameter  when  working  against  a  pressure  of  0.4 
of  an  ounce  per  square  inch. 

Here  the  diameter  of  the  inlet  is  0.625  of  the 
diameter  of  the  wheel,  and  from  Table  HA  we  see 
that  the  capacity  is  8730. 

From  Table  II.  we  see  that  the  same  fan  with 
an  inlet  whose  diameter  is  0.707  of  the  diameter 
of  the  wheel  has  a  capacity  equal  to  12700;  nearly 
50  per  cent,  more  with  the  larger  inlet  than  with 
the  smaller. 


74  CENTRIFUGAL    FANS. 

Blast  Area.  In  the  discussion  of  the  capacity 
of  a  fan  nothing  has  been  said  as  to  the  size  or 
area  of  the  outlet  orifice,  although  it  has  been  as- 
sumed that  it  was  large  enough  to  allow  the  air 
to  pass  out.  When  the  outlet  orifice  is  small,  the 
air  will  pass  out  of  it  with  a  velocity  equal  to  that 
of  the  tips  of  the  floats.  If  the  opening  be  made 
larger  and  larger  the  air  will  continue  to  pass  out 
with  a  velocity  equal  to  that  of  the  tips  of  the 
floats,  until  the  area  of  the  outlet  multiplied  by 
its  proper  coefficient  of  discharge  becomes  equal  to 
what  is  known  as  the  Blast  Area  of  the  fan.  And 
if  the  area  of  the  outlet  be  made  larger,  the  pres- 
sure in  the  housing  will  become  less  and  the  air 
will  pass  out  with  a  velocity  less  than  that  of  the ' 
tips  of  the  floats. 

The  Blast  Area  may  be  defined  then  as  that 
theoretical  area  of  outlet  which  will  allow  the 
maximum  quantity  of  air  to  pass  out  while  the 
pressure  in  the  housing  remains  equal  to  that  cor- 
responding to  the  velocity  of  the  tips  of  the  floats. 

By  "  theoretical  area  "  is  meant  the"  area  of 
an  opening  whose  coefficient  of  discharge  is  1. 

When  the  pressure  in  the  housing  is  equal  to 
that  corresponding  to  the  velocity  of  the  tips  of 
the  floats,  the  velocity  of  the  air  passing  through 
the  outlet  is  equal  to  the  velocity  ,of  the  tips  of 
the  floats.  Hence  the  blast  area  in  square  feet 
multiplied  by  the  velocity  of  the  tips  of  the  floats 
in  feet  per  minute,  must  be  equal  to  the  capacity 


BLAST    AREA.  75 

of  the  fan  or  the  maximum  quantity  of  air  dis- 
charged by  the  fan  when  working  against  a  pres- 
sure equal  to  that  corresponding  to  the  velocity 
of  the  tips  of  the  floats. 

Hence,  calling  A  the  blast  area  in  square  feet, 
and  using  the  same  notation  as  before,  we  have 
that  the  velocity  of  the  tips  of  the  floats  in  feet 
per  minute  is  n  D  N ;  and  the  capacity  C  of  the 
fan  is 

(22)  C  =  7i  D  N  A 
But  from  (15)  we  know  that 

C  =  1.38r*D3N 
and  putting  this  value  of  C  in  (22)  we  have 

xDNA  =  l.38r*D*N 
From  which  we  get  " 

(23)  A  =  0.44  r3  D2 

Equation  (23)  gives  the  blast  area  in  square 
feet  for  single  inlet  fans,  but  because  of  the  im- 
pediments to  the  flow  of  air  through  the  inlets  of 
double  inlet  fans,  as  has  been  explained  before,  it 
is  .well  to  assume  that  for  most  commercial  double 
inlet  fans  the  blast  area  is  the  same  as  for  single 
inlet  fans.  If  it  were  possible  to  have  a  double 
inlet  fan  with  each  inlet  as  open  and  free  for  the 
admission  of  air  as  is  usually  the  case  with  a  single 
inlet  fan,  the  capacity  and  also  the  blast  area  of 
such  a  fan  would  be  double  what  it  is  for  a  single 


76  CENTRIFUGAL   PANS. 

inlet  fan.  The  only  advantage  to  be  gained  in 
buying  a  double  inlet  fan  for  heating  or  ventilating 
work  is  the  possibility  of  getting  some  increase  of 
capacity  and  blast  area  by  reason  of  the  fact  that 
the  two  inlets  may  offer  a  larger  area  for  the  ad- 
mission of  air  than  one,  and  whatever  increase 
there  may  be,  is  simply  so  much  increase  in  the 
factor  of  safety  used. 

If  (23)  be  multiplied  by  144  we  have  A',  the 
blast  area  in  square  inches,  is 

(24)  A'  =--  144  A  «  63.4r3Z72 

If  r  is  equal  to  \/2"or  0.707,  (23)  and  (24) 
become, 

(25)  A  =  0.155Z?2 

(26)  A '  =  22.4  D2 

If  r  is  equal  to  f  or  0.625,  (23)  and  (24)  become, 

(27)  A  =  0.107£>2 

(28)  A'  =  15.5  D'2 

Table  III.  gives  the  blast  areas  in  square  feet 
and  in  square  inches  for  fan  wheels  of  different 
diameters,  for  /-  equal  to  0.707  and  for  r  equal  to 
0.625.  In  this  table  the  square  feet  are  given  to 
the  nearest  tenth;  and  the  square  inches  to  the 
nearest  five  below  1000,  and  to  the  nearest  50 
above  1000. 


BLAST     AREA. 


77 


TABLE  III. 
Blast  areas. 


r  =  0.707 

r  =  0.625 

Diameter 

Blast  Area  in 

Blast  Area  in 

of  wheel 

in  feet 

sq.  ft.                sq.  in. 

sq.  ft.                 sq.  in. 

A                       A' 

A                       A' 

3 

1.4 

200 

0.96 

140 

3* 

1.9 

275 

1.3 

190 

4 

2.5 

360 

1.7 

250 

4* 

3.1 

455 

2.2 

315 

5 

3.9 

560 

2.7 

390 

5* 

4.7 

675 

3.2 

470 

6 

5.6 

805 

3.9     , 

560 

6* 

6.5 

945 

4.5 

655 

7 

7.6 

1100 

5.3 

760 

8 

9.9 

1450 

6.9 

990 

9 

12.6 

1800 

8.7 

1250 

10 

15.5 

2250 

10.7 

1550 

11 

18.8 

2700 

13.0 

1900 

12 

22.3 

3200 

15.4 

2250 

In  ordinary  heating  and  ventilating  work  the 
blast  area  is  a  matter  of  small  consequence,  but 
in  exhauster  work  for  mills  and  factories  where  it 
is  necessary  to  choose  a  fan  to  carry  away  shavings, 
dust  and  dirt,  and  where  the  velocity  of  the  air 
in  the  ventilating  ducts  and  flues  must  be  quite 
large,  the  blast  area  is  of  great  importance  and 
plays  a  considerable  part  in  the  considerations 
which  decide  what  size  of  fan  to  use. 

The  area  of  the  inlet,  as  has  been  said  before,  is 

— j — •,    and  the  coefficient  of  discharge   for   the 
inlet  has  been  assumed  to   be  0.56;  so   that  the 


78  CENTRIFUGAL    FAXS. 

theoretical  area  of  the  inlet  or  the  product  of  the 
inlet  area  and  its  coefficient  of  discharge  is 


0.56  n  r2  D2  .    2  n2 
; =  0.44  r2  D2 


But  from  (23)  we  know  that  the  blast  area  is 
0.44  r3  D2.  Therefore,  the  blast  area,  A,  is  equal 
to  the  theoretical  inlet  area  multiplied  by  r\  and 
conversely,  the  theoretical  inlet  area  is  equal  to 

*  A 

the  blast  area  divided  by  r,  or  — 

J  r. 


Effect  of  Outlet  on  Capacity.  When  the  theo- 
retical outlet  area  of  a  fan,  that  is  the  product  of 
the  area  of  the  outlet  multiplied  by  its  proper 
coefficient  of  discharge,  is  less  than  the  blast  area, 
the  pressure  in  the  housing  is  that  corresponding 
to  the  velocity  of  the  tips  of  the  floats;  and  the 
quantity  of  air  discharged  is  equal  to  the  velocity 
of  the  tips  of  the  floats  multiplied  by  the  product 
of  the  area  of  the  outlet  and  its  coefficient  of  dis- 
charge. Let  a  be  the  area  of  the  outlet,  c  its 
coefficient  of  discharge,  and  Cxthe  number  of  cubic 
feet  of  air  discharged  per  minute.  The  velocity  in 
feet  per  minute  of  the  tips  of  the  floats  is  n  D  N, 
where  as  before,  D  is  the  diameter  in  feet  of  the 
wheel,  and  N  is  the  number  of  revolutions  per 
minute. 


EFFECT  OF  OUTLET  ON  CAPACITY.       79 

Hence  the  expression  for  the  number  of  cubic 
feet  of  air  delivered  by  a  fan  when  the  product  of 
the  area  of  the  outlet  and  its  coefficient  of  discharge 
is  less  than  the  blast  area,  is 

(29)  C,  =  TT  D  N  c  a 

But  from  (22)  we  know  that  the  expression  for 
the  capacity  C,  of  the  fan  is 

C  =  TT  D  N  A 
From  this  we  get 


and  this  value  of  K  D  N  put  in  (29)  gives 
(30)  Ct  -  ^ 

If  c  a  is  equal  to  A,  Cl  becomes  equal  to  C. 

EXAMPLE  : — Determine  the  number  of  cubic  feet 
of  air  discharged  per  minute  by  a  fan  with  a  9-foot 
wheel  working  against  a  pressure  in  the  housing  of 
0.3  ounce  per  square  inch  and  with  an  outlet  whose 
area  is  11  square  feet  and  whose  coefficient  of  dis- 
charge is  0.8.  The  diameter  of  the  inlet  is  to  be 
assumed  to  be  0.707  of  the  diameter  of  the  wheel. 

Here  a  is  11  and  c  is  0.8,  so  that  c  a  is  8.8. 


80  CENTRIFUGAL   FANS. 

From  Table  III.  it  is  seen  that  the  blast  area  of  a 
9-foot  wheel  is  12.6  square  feet,  and  hence  accord- 
ing to  the  conditions  of  the  example,  the  area  of 
the  outlet  multiplied  by  its  coefficient  of  discharge 
is  less  than  the  blast  area.  The  value  of  Cl  could 
be  calculated  direct  by  (29)  if  we  knew  N,  but 
as  N  is  not  given  and  we  have  not  yet  explained 
how  to  find  it  when  the  pressure  is  known,  we 
shall  use  (30)  to  find  C\. 

From  Table  II.  we  find  that  C  for  a  9-foot  wheel 
working  against  a  pressure  of  0.3  ounce  is  35300. 
Hence  putting  the  values  of  c  a,  A ,  and  C  in  (30) 
we  have 

caC       8.8  X  35300 
1  =      A  12.6 

=  24700. 

When  the  product  of  the  area  of  the  outlet 
multiplied  by  its  coefficient  of  discharge  is  greater 
than  the  blast  area  the  problem  of  determining 
the  number  of  cubic  feet  of  air  discharged  per 
minute  is  much  more  complicated  than  when  the 
product  of  the  area  of  the  outlet  multiplied  by  its 
coefficient  of  discharge  is  less  than  the  blast  area. 
When  the  area  of  the  outlet  multiplied  by  its  co- 
efficient of  discharge,  or  c  a,  is  less  than  the  blast 
area,  A,  the  number  of  cubic  feet  of  air  discharged 
per  minute  is  less  than  the  capacity  of  the  fan; 


EFFECT  OF  OUTLET  ON  CAPACITY.        81 

but  when  c  a  is  greater  than  A ,  the  number  of 
cubic  feet  of  air  discharged  per  minute,  which  we 
shall  call  C2,  is  greater  than  the  capacity  of  the 
fan.  In  order  that  the  number  of  cu&ic  feet  of 
air  discharged  by  a  fan  shall  be  greater  than  the 
capacity  of  the  fan,  the  velocity  through  the  inlet 
must  be  greater  than  the  velocity  of  rotation  of 
:,he  points  of  the  floats  at  the  inlet,  because  the 
capacity  of  a  fan.,  is  as  shown  before,  the  number 
of  cubic  feet  of  air  which  will  enter  through  the . 
inlet  per  minute  with  a  velocity  equal  to  that  of 
the  points  of  the  floats  at  the  inlet. 

As  has  been  said  when  discussing  vortexes  with 
a  radial  flow  from  the  center  outward  towards  the 
periphery,  when  the  radial  velocity  at  the  inlet 
is  greater  than  the  velocity  of  rotation  at  the 
inlet,  the  pressure  in  the  housing  or  casing  is  less 
than  the  pressure  corresponding  to  the  velocity  of 
the  tips  of  the  blades  or  floats.  Further,  when 
the  velocity  through  the  inlet  is  greater  than  the 
radial  velocity  at  the  inlet,  and  is  also  greater  than 
the  velocity  of  rotation  of  the  points  of  the  floats 
at  the  inlet,  the  pressure  in  the  housing  is  less  than 
that  due  to  the  velocity  of  rotation  of  the  tips  of 
the  floats. 

Let  P  be  the  pressure  corresponding  to  the  ve- 
locity of  the  tips  of  the  floats;  pi,  the  pressure 
corresponding  to  the  velocity  through  the  inlet, 
or  the  radial  velocity  at  the  inlet  if  it  be  less  than' 
the  velocity  through  the  inlet;  p2,  the  pressure 


82  CENTRIFUGAL    FANS. 

corresponding  to  the  velocity  of  rotation  of  the 
points  of  the  floats  at  the  inlet  ;  and  p,  the  pressure 
in  the  housing  making  the  air  flow  out  through  the 
outlet.  Then  from  (11)  we  have 

(31)  p  =  P  +  pf-pt 

The  air  flows  out  of  the  housing  with  a  velocity 
due  to  the  pressure  p,  which  according  to  (3)  is 
equal  to  5200  \/  pm  And  since  the  area  of  the  out- 
let is  a  and  its  coefficient  of  discharge  is  c,  the 
quantity  of  air  flowing  out  per  minute  is 

(32)  C2  =  5200  a  c  Vp~ 

Now  the  air  flows  into  the  fan  through  the  inlet 
with  a  velocity  due  to  the  pressure  plt  which  accord- 
ing to  (3)  is  equal  to  5200  \/~p[m  And  since  as  has 
been  shown  when  discussing  the  blast  area,  the 

inlet  area  multiplied  by  its  coefficient  of  discharge 

A 

is  equal  to  the  blast  area,  A,  divided  by  r,  or  —  , 

r 

the  quantity  of  air  entering  the  fan  which  is  the 
same  as  the  quantity  which  flows  out  of  the  hous- 
ing, is 


5200  A 
(33)  C2  = 


but  from  (31)  we  have 


EFFECT    OF    OUTLET    ON    CAPACITY.  83 

putting  this  value  of  p±  in  (33)  we  have 
(34)  C2  =  ™>A^P±h  '.-  P. 

From  (32)  and  (34)  we  have 


Solving  this  equation  for  />,  we  get 

P  +  P> 
(35)  ^    -          a2  c2  r2 

A2 

Now  P  is  the  pressure  due  to  the  velocity  in 
feet  per  minute  of  the  tips  of  the  floats,  which  is 
n  D  N;  and  p2,  is  the  pressure  due  to  the  velocity 
in  feet  per  minute  of  points  on  the  floats  at  the 
inlets,  which  is  n  r  D  N.  Therefore  we  have  from 

(5) 

p  = 


5200 

(nr  DN 
:  V    5200 

And  from  these  we  get 


52002 


84  CENTRIFUGAL   FANS. 

If  we  put  this  value  of  P-f£2  in  (35)  and  solve 
for  p  we  get 

(36)  P  =  ~     y^-^7^2 

A2 

And  finally  this  value  of  p  in  (32)  gives  as  the 
expression  for  C2 


(37) 


~~ 

I 

But  from  (22)  we  get 

*DN  =  ^ 
and  this  value  of  x  D  N  in  (37)  give 

'  TT72" 


4    xi  -    — 
\          a2 
~ 


If  the  area  of  the  outlet  multiplied  by  its 
coefficient  of  discharge  is  made  equal  to  the  blast 
area,  that  is  if  a  c  is  made  equal  to  A  ,  we  see  from 
(38)  that  C2  becomes  equal  to  C. 

Equation  (38)  shows  that,  if  a  fan  wheel  be  run 
at  such  a  speed  as  to  give  a  capacity  C  against  a 


EFFECT   OF    OUTLET    ON    CAPACITY. 


85 


certain  pressure  when  the  outlet  is  the  blast  area, 
the  quantity  of  air  delivered  by  the  fan  without 
any  change  of  speed  but  with  a  larger  outlet  will 
be  increased  by  the  value  of  the  fraction 


ac 


14. 


This  fraction  involves  only  the  values  of  a, 
c,  r,  and  A,  and  it  is  therefore  possible  to  make  a 

table  giving  its  value  for  different  values  of     —r 
and  r.     If  we  call  this  fraction  B,  we  have  from  (38) 
(39)  C2  =  C  B 

Table  IV.  gives  the  value  of  B  for  different 
values  of  -r-  and  for  r  equal  to  0.5,  0.625  and 
0.707.  . 

TABLE  IV. 


a  c 
A 

B  for 
r  =  0.5 

B  for 
r  =  0.625 

B  for 
r  =  0.707 

1.0 

1.00 

1.00 

1.00 

1.2 

1.15 

1.13 

1.12 

1.4 

1.28 

1.24 

1.22 

1.6 

1.40 

1.33 

1.30 

1.8 

1.50 

1.41 

1.36 

2.0 

1.58 

1.47 

1.41 

86  CENTRIFUGAL    FANS. 

Table  IV.  shows  how  the  value  of  r  affects  the 

value  of  B  for    the    same  value  of  —          If,  for 

j\. 

instance,  —r   is    1.6,  the    table    shows    that    for  r 
J\. 

equal  0.5,  that  is  the  diameter  of  the  inlet  is  one- 
half  the  diameter  of  the  fan,  B  is  1.40;  while  if  r 
be  0.707,  B  is  1.30.  It  must  be  carefully  borne  in 
mind  that,  as  has  been  said  so  often  before,  when 
the  outlet  is  increased  so  that  a  c  is  greater  than 
A ,  the  quantity  of  air  delivered  by  the  fan  will  be 
increased  and  made  greater  than  the  capacity  of 
the  fan,  but  the  pressure  in  the  housing  near  the 
outlet  will  be  less  than  that  due  to  the  velocity 
of  the  tips  of  the  floats. 

As  an  example,  we  may  consider  the  case  of  a 
fan  with  an  8-foot  wheel  for  which  r  is  equal  to 
0.707.  Such  a  fan,  when  a  c  is  equal  to  A,  work- 
ing against  a  pressure  of  0.3  of  an  ounce,  has  a 
capacity  according  to  Table  II.,  of  28000  cubic 
feet  per  minute.  That  is  to  say,  C  is  28000. 
Now  suppose  the  speed  of  the  wheel  is  not  changed 

at  all,  but  the  outlet  is   made  larger  so   that  —r 

f\. 

is  equal  to  1.4.     From  Table  IV.  we  find  that  when 

^  is  1.4,  and  r  is  0.707,  B  is  1.30.  And  from 
J\ 

(39)  we  get 

C2  =  CB 

=  28000x1.30 
=  36400 


AIR    PER    REVOLUTION.  87 

Air  Per  Revolution.  It  is  sometimes  conven- 
ient to  be  able  to  determine  the  number  of  cubic 
feet  of  air  which  a  fan  of  a  given  diameter  of  wheel 
and  inlet  will  deliver  per  revolution. 

From  (22)  we  know  that  when  the  theoretical 
area,  a  c,  of  the  outlet  is  equal  to  the  blast  area,  A, 
the  number  of  cubic  feet  of  air  delivered  is  equal 
to  the  capacity  of  the  fan  and  is 

(40)  C  =  nDN  A 

From  (29)  we  know  that  when  a  c  is  less  than 
A ,  the  number  of  cubic  feet  of  air  delivered  is 

(41)  Cl  =  7i  D  N  a  c 

And  from  (37)  we  know  that  when  a  c  is 
greater  than  A,  the  number  of  cubic  feet  delivered 
is 


(42)  C2  =  n  D  N  a  c  J 

1  + 


1  +  r2 


It  is  evident  that  if  we  divide  (40),  (41)  and 
(42)  by  N,  the  number  of  revolutions  per  minute 
of  the  fan  wheel,  we  shall  have  the  number  of 
cubic  feet  of  air  delivered  per  revolution  for  the 
different  relative  values  of  a  c,  and  A.  Therefore, 
let  q  be  the  number  of  cubic  feet  of  air  delivered 


88  CENTRIFUGAL   FANS. 

per  revolution,  and  from  (40),  (41)  and  (42)  we  get 

7i  D  A ,  when  a  c  equals  A  ; 

n  D  a  c,  when  a  c  is  less  than  A  ; 


(43)  q- 


is 


1  +  a'c\r\     when    a 
greater  than  A. 


If  we  let  n  D  A  be  represented  by  <?',  and  re- 
member that  in  (39)  we  have  designated  the  frac- 


tion 


ac 
~A 


by  the   letter  5,  from    (43), 


we  get 


(44)        q  - 


gr,  when  a  c  equals 
a 


,when  a  c  is  less  than  A  ; 
q'  B,  when  a  c  is  greater  than  A. 


The    value   of  B  for    different    values   of 


ac 

~A 


is  given  in  Table  IV. 

q'  is  the  air  delivered  per  revolution  of  the 
wheel  when  the  fan  is  working  at  its  capacity 
and  depends  upon  the  blast  area  of  the  fan  wheel ; 


AIR    PER    REVOLUTION. 


89 


and  the  blast  area,  A,  as  has  been  shown,  depends 
upon  the  ratio,  r,  of  the  diameter  of  the  inlet  to 
the  diameter  of  the  wheel.  To  determine  q'  for 
any  given  fan  all  that  is  necessary  is  to  multiply 
the  blast  area  of  the  wheel  as  given  by  Table  III. 
by  TT  times  the  diameter  of  the  wheel.  The  blast 
area  must,  of  course,  be  in  square  feet,  and  the 
diameter  of  the  wheel  must  be  in  feet. 

Table  V.  gives  the  value  of  q'  for  fans  with  wheels 
of  different  diameters,  and  for  r,  the  ratio  of  the 
diameter  of  the  inlet  opening  to  the  diameter  of  the 
wheel,  equal  to  0.625  and  to  0.707. 


TABLE  V. 

Cubic  feet  of  air  per  revolution. 


Diameter 

Diameter 

of  wheel 

r  =  0.625 

r-0.707 

of  wheel 

r  =  0.625 

r  =  0.707 

in  feet. 

Q' 

q' 

in  feet. 

q' 

q' 

3 

9.1 

13.2 

e* 

92 

133 

3* 

14.3 

20.9 

7 

116 

,     167 

4 

21.4 

31.4 

8 

173 

250 

*i 

31 

44 

9 

245 

355 

5 

42 

61 

10 

335 

485 

5* 

55 

81 

11 

450 

650 

6 

74 

105 

12 

580 

840 

Table  V.  may  be  used  to  determine  the  num- 
ber of  revolutions  at  which  the  wheel  of  a  fan  must 
be  run  to  deliver  a  given  number  of  cubic  feet  of 
air  per  minute  when  the  theoretical  outlet  area, 
a  c,  is  equal  to  the  blast  area,  A. 


90  CENTRIFUGAL     FANS. 

EXAMPLE:  —  What  must  be  the  speed  of  a  fan 
wheel  whose  diameter  is  7  feet,  and  whose  inlet 
diameter  is  59^  inches,  in  order  to  deliver  25000 
cubic  feet  of  air  a  minute. 


Here  r  is       '     or  0.707.     We  shall  assume  that 


the  theoretical  outlet  area  is  equal  to  the  blast 
area.  From  Table  V.  we  see  that  when  r  is  0.707 
a  7-foot  wheel  will  deliver  167  cubic  feet  of  air  per 
revolution.  Hence  to  deliver  25000  cubic  feet  of 
air  per  minute  a  7-foot  wheel  must  make  as  many 
revolutions  per  minute  as  167  is  contained  in 
25000,  that  is 

*,       .25000 
167 
=  150. 


CHAPTER  VI. 


Pressure.  When  the  area  of  the  outlet  multi- 
plied by  its  coefficient  of  discharge  is  equal  to  or 
less  than  the  blast  area,  the  pressure  in  the  housing 
is  P,  that  corresponding  to  the  velocity  of  the  tips 
of  the  floats;  and  since  the  velocity  of  the  tips  of 
the  floats  is  n  D  N,  we  have  from  (3) 


(45)  n  D  N  =  5200  - 
From  this  we  get 

(46)  D  N  =  1650  VP~ 
and  also 

1650 


(47) 


D 


EXAMPLE: — Determine  the  number  of  revolu- 
tions per  minute  which  must  be  made  by  a  fan 
with  a  6-foot  wheel  to  give  a  pressure  of  0.6  of  an 

91 


92  CRNTRIFUGAL     FANS. 

ounce  when  the  theoretical  area  of  the  outlet  is 
equal  to  or  less  than  the  blast  area. 
Here  P  is  0.6  and  D  is  6,  so  that 

1650  x/O6 
6 

=  213 
If  (46)  be  solved  for  P  we  get 


This  equation  enables  us  to  determine  the  pres- 
sure in  ounces  per  square  inch  in  the  housing  of  a 
fan  when  we  know  the  diameter  of  the  wheel  and 
the  number  of  revolutions  made  by  it  per  minute., 

EXAMPLE.  —  Determine  the  pressure  in  ounces 
per  square  inch  in  the  housing  of  a  fan  having  an 
8-foot  wheel  running  at  150  revolutions  per  min- 
ute, when  the  theoretical  outlet  is  equal  to  or  less 
than  the  blast  area. 

Here  D  is  8,  N  is  150,  and,  therefore, 


78x150  V 
=  \    1650    / 


=  0.53 

Table  VI.  is  calculated  from  (47)  and  gives  the 
number  of  revolutions  per  minute  at  which  wheels 
of  different  diameters  must  be  run  in  order  to  give 
various  pressures  in  ounces  per  square  inch  when 
the  theoretical  outlet  area  is  equal  to  or  less  than 
the  blast  area  of  the  wheel. 


PRESSURE. 


93 


TABLE  VI. 

Number  of  revolutions  for  different  pressures. 


Diam  . 

Pressure  per  square  inch  in  ounces. 

in  feet. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

3 

174 

246 

301 

348 

389 

426 

460 

492 

522 

5,rO 

B* 

149 

211 

258 

293 

334 

365 

394 

422 

447 

471 

4 

130 

185 

226 

261 

292 

320 

345 

369 

391 

413 

4* 

116 

164 

201 

232 

259 

284 

307 

328 

348 

366 

5 

104 

148 

181 

209 

234 

256 

276 

295 

313 

330 

5i 

95 

134 

164 

190 

212 

232 

251 

268 

284 

300 

6 

87 

123 

151 

174 

195 

213 

230 

246 

261 

275 

6* 

80 

114 

139 

161 

180 

197 

212 

227 

241 

254 

7 

75 

105 

129 

149 

167 

183 

197 

211 

224 

236 

8 

65 

92 

113 

131 

146 

160 

173 

184 

196 

206 

9 

58 

82 

101 

116 

130 

142 

154 

164 

174 

183 

10 

52 

74 

91 

105 

117 

128 

138 

148 

157 

165 

11 

47 

67 

82 

95 

106 

116 

126 

134 

142 

150 

12 

44 

62 

75 

87 

97 

108 

115 

123 

131 

138 

Table  VI.  should  be  us  3d  in  connection  with 
Tables  II.  and  HA.  From  Tables  II.  and  HA  we 
can  find  the  size  of  wheel  required  to  deliver  a 
given  quantity  of  air  per  minute  at  a  given  pres- 
sure, then  from  Table  VI.  we  can  find  the  number 
of  revolutions  the  wheel  must  make  per  minute. 

EXAMPLE: — Determine  the  diameter  of  wheel 
required  to  deliver  50000  cubic  feet  of  air  per 
minute  against  a  pressure  of  0.7  of  an  ounce  per 
square  inch.  The  diameter  of  the  inlet  is  0.707 
of  the  diameter  of  the  wheel. 

Turning  to  Table  II.  we  find  that  a  9-foot 
wheel  will  deliver  only  54200;  and  a  10-foot  wheel 
will  deliver  67000  cubic  feet.  We  shall  use,  there- 


94  CENTRIFUGAL    PANS. 

fore,  a  9-foot  wheel.  Turning  now  to  Table  VI., 
we  find  that  a  9-foot  wheel  must  make  154  revolu- 
tions per  minute  to  give  a  pressure  of  0.7  of  an  ounce. 
When  the  area  of  the  outlet  multiplied  by  its 
coefficient  of  discharge  is  greater  than  the  blast 
area,  that  is  when  a  c  is  greater  than  A,  we  have 
from  (36)  that  the  pressure  in  the  housing  is 


(49) 


52002 


From  which  we  get 


(50) 


From  (45)   we  get,  by  solving  for  P, 


p  — 

52002 


PRESSURE.  95 

7T2  D2  N2 

Hence    substituting    in    (49)   for —  its 

5200 

value  we  have 

(52)  p  =  — 


a2  c2  r2 
~2~~ 


Equation  (52)  shows  the  effect  on  the  pressure 
of  increasing  the  outlet  area  without  changing  the 
speed  or  number  of  revolutions  per  minute.  That 
is  to  say  if  a  fan  having  a  wheel  of  a  given  diam- 
eter is  run  at  a  certain  number  of  revolutions,  it 
will  give  a  pressure  in  ounces  per  square  inch 
equal  to  P  when  the  outlet  is  equal  to  the  blast 
area ;  but  if  the  outlet  is  made  larger  than  the  blast 
area  and  the  wheel  be  run  at  the  same  speed  as 
before,  the  pressure  then  will  be  p  as  given  by 
(52).  In  using  (52)  it  must  be  remembered  that  * 
P  is  the  pressure  the  wheel  would  give  if  the 
theoretical  outlet  area  a  c  were  equal  to  the  blast  / 
area,  and  the  value  of  P  to  be  used  in  (52)  must 
be  calculated  by  (48)  or  taken  from  Table  VI. 

1  +  r2 

If  we  let  F  represent  the  fraction    0    ,    , 

a2  c2  r2, 

(51)  becomes 

(53)  N=    ^~ 
and   (52)  becomes 

(54)  p  -  P  F 


96 


CENTRIFUGAL    FANS. 


Table  VII.  gives  the  value  of  F  for  different 


values  of   —r    and  for  r  equal  0.5,  0.625  and  0.707. 


TABLE  VII. 


ac 
A 

Value  of  F  for 

r  =  0.5 

r  =  0.625 

r  =  0.707 

1.0 

1.00 

1.00 

1.00 

1.2 

0.92 

0.89 

0.87 

1.4 

0.84 

0.79 

0.76 

1.6 

0.76 

0.70 

0.66 

1.8 

0.69 

0.61 

0.57 

2.0 

0.63 

0.54 

0.50 

EXAMPLE: — Determine  the  speed  at  which  a 
9-foot  wheel  must  be  run  in  order  to  give  a  pres- 
sure per  square  inch  of  0.5  an  ounce  when  the 
outlet  is  equal  to  the  blast  area,  and  also  when  the 
outlet  is  1.6  times  the  blast  area.  Assume  that 
the  diameter  of  the  inlet  is  0.625  of  the  diameter 
of  the  wheel. 

Here  we  have -D  is  9  feet ;  p  is  0.5;    -j-    is    1.6; 

J\. 

and  r  is  0.625.  The  number  of  revolutions  the 
wheel  must  make  when  the  outlet  is  equal  to  the 
blast  area  may  be  calculated  by  (47)  or  may  be 
found  from  Table  VI.  From  Table  VI.  we  find 
that  a  9-foot  wheel  must  make  130  revolutions 
per  minute  to  give  a  pressure  of  0.5  of  an  ounce 


PRESSURE.  97 

when  the  theoretical  outlet  is  equal  to  the  blast 
area. 

Table  VII.  shows   that   when  —   is    1.6,     and 

r  is  0.625,  F  is  0.70. 

Hence  from  (53)  we  have 

1650     l~p 
D    Yl? 

1650      1 05Q 
9      \0770 

=  155 

Equation  (54)  enables  us  to  determine  the 
effect  on  the  pressure  given  by  a  fan  wheel  of  in- 
creasing the  outlet  area  without  changing  the  num- 
ber of  revolutions.  Thus  in  the  last  example  we 
saw  that  a  9-foot  wheel  for  which  r  is  0.625,  would 
give  a  pressure  of  0.5  of  an  ounce  when  making 
130  revolutions.  We  also  saw  from  Table  VII. 

that  for  r  equal  to  0.625,    and  -r-     equal    to    1.6, 

F  was  0.70.  Now  when  F  is  0.70  and  P  is  0.50, 
equation  (54)  shows  that  a  9-foot  wheel  making 
130  revolutions  and  the  theoretical  area  of  the 
outlet  equal  to  1.6  the  blast  area,  will  give  a  pres- 
sure only  of 


98  CENTRIFUGAL    PANS. 

p  =  PF  =  0.5x0.70 
=  0.35 

In  most  fan  problems  which  arise  in  actual 
work  the  outlet  of  the  fan  housing  is  usually  con- 
nected to  a  chamber  in  which  it  is  desired  a  certain 
pressure  shall  be  maintained. )  In  all  of  such  cases 
the  outlet  to  be  considered  in  calculating  the 
value  of  a  c  to  be  used  in  the  equations  for  p,  is 
not  the  outlet  from  the  fan  housing  but  the  outlet  from 
the  chamber  in  which  the  pressure  is  desired.  The 
outlet  to  be  considered  is  always  the  one  leading 
into  the  atmosphere,  i  The  pressure  in  the  chamber 
will  be  somewhat  lesis  than  in  the  housing  because 
of  losses  due  to  friction,  shape  of  housing,  con- 
nections of  duct  between  the  housing  and  the  cham- 
ber, etc.,  but  ordinarily  the  chamber  is  located  so 
close  to  the  fan  that  the  loss  of  pressure  between 
the  housing  and  the  chamber  is  small. 

Tables  IV.  and  VII.  enable  us  to  determine 
the  full  effect  of  increasing  the  outlet  of  a  fan  so 
as  to  make  the  theoretical  outlet  greater  than  the 
blast  area.  For  instance,  Table  IV.  shows  that  if 
the  outlet  of  a  fan  for  which  r  is  0.625,  be  increased 

so  that  -r-  is  1.2,    the   number  of   cubic   air  dis- 
J\. 

charged  per  minute  will  be  1.13  what  it  is  when 
the  outlet  is  equal  to  the  blast  area;  and  Table  VII. 
shows  that  the  pressure  will  be  only  0.89  of  what 


WORK.  99 

it  is  when  the  outlet  is  equal  to  the  blast  area. 
In  other  words,  to  increase  the  outlet  of  a  fan 
for  which  r  is  0.625  so  that  the  theoretical  area 
is  20  per  cent,  greater  than  the  blast  area  brings 
about  an  increase  of  13  per  cent,  in  the  quantity 
of  air  delivered  per  minute  by  the  fan  with  a  de- 
crease of  11  per  cent,  in  the  pressure.  If  r  were 
0.5,  to  increase  the  outlet  so  as  to  make  it  20  per 
cent,  greater  than  the  blast  area  would  bring  about 
an  increase  of  15  per  cent,  in  the  quantity  of  air 
delivered  and  a  decrease  of  only  8  per  cent,  in 
the  pressure.  While  if  r  were  0.707,  a  correspond- 
ing increase  in  the  outlet  would  mean  an  increase 
of  12  per  cent,  in  the  quantity  of  air  discharged 
with  a  decrease  of  13  per  cent,  in  the  pressure. 

The  pressure  which  can  be  produced  by  a  cen- 
trifugal fan  or  the  pressure  under  which  air  or 
gases  can  be  delivered,  is  limited  only  by  the 
velocity  at  which  the  wheel  can  be  safely  run ;  and 
this  is  limited  by  the  materials  used  in  the  con- 
struction of  the  wheel  and  the  care  and  skill  with 
which  the  parts  are  put  together. 

Work.  (  The  work  done  per  minute  in  moving 
air  is  equal  to  the  product  of  the  number  of  cubic 
feet  of  air  moved  per  minute  multiplied  by  the 
sum  of  the  pressure  in  the  housing  near  the  outlet 
and  the  pressure  corresponding  to  the  velocity  per 
minute  of  the  air  as  it  enters  the  fan.\  The  pres- 
sures must  be  not  ounces  per  square  inch  but 


100  CENTRIFUGAL    FANS. 

pounds  per  square  foot;  and  if  the  velocity  of  the 
air  through  the  inlet  is  less  than  the  radial  velocity 
at  the  inlet,  then  the  pressure  corresponding  to 
the  radial  velocity  must  be  taken  instead  of  the 
pressure  corresponding  to  the  velocity  through  the 
inlet. 

As  before,  let  p  be  the  pressure  in  ounces  per 
square  inch  in  the  housing;  P  the  pressure  in 
ounces  per  square  inch  corresponding  to  the  velo- 
city of  the  tips  of  the  floats  of  the  wheel;  p±1  the 
pressure  in  ounces  per  square  inch  corresponding 
to  the  velocity  through  the  inlet  or  the  radial 
velocity  at  the  inlet,  whichever  is  the  larger;  and 
p2,  the  pressure  in  ounces  per  square  inch  corre- 
sponding to  the  velocity  of  the  points  of  the  floats 
at  the  inlet.  Then  the  sum  of  the  pressure  in 
the  housing  and  the  pressure  corresponding  to  the 
velocity  through  the  inlet  is  p  +  p^  This  sum, 
however,  is  in  ounces  per  square  inch;  and  to  re- 
duce it  to  pounds  per  square  foot  it  must  be 
divided  by  16,  since  there  are  sixteen  ounces  to 
a  pound,  and  multiplied  by  144,  since  there  are 
144  square  inches  to  a  square  foot.  Therefore, 
the  sum  of  the  pressure  in  the  housing  and  the 
pressure  corresponding  to  the  velocity  through 
the  inlet,  when  expressed  in  pounds  per  square 
foot  is 


WORK.  101 

But  it  has  been  shown  before  ;that,  when  the 
outlet  is  equal  to  the  blast  area^'tife:  hupilDer  o( 
cubic  feet  of  air  discharged  by  I'he^fan  per,  rnitmte 
is  the  capacity  C  ;  p  is  equal  to  P  ;'  and  "$[  is  equal 
to  p2.  Hence,  the  work  done  per  minute  is 


But  from  (48)  we  know  that 


p  =   I 

\1650. 


and  since  the  velocity  through  the  inlet  is  TT  r  D  N, 
we  have 


..rD  "' 
p2  ~  1     5200 


\1650  / 

Therefore  P  +  p2  is  equal  to  P  (l  +  r2)  and  the 
expression  for  the  work  done  per  minute  becomes 


9C  (P  +  P2)  =  9CP  (1+r2) 

Now  the  horse  power  expended  on  the  air  is 
equal  to  the  work  done  on  it  per  minute  divided 


102  CENTRIFUGAL    FANS. 

by  33000.     And.  if  we  designate  this  horse  power 
by  K,  we  JiaVs     ' 


33000 


3670 


It  must  be  remembered  that  K  is  only  the 
horse  power  required  to  move  the  air  and  does 
not  include  any  part  of  the  power  required  to 
overcome  the  friction  of  the  wheel  in  its  bearings. 

If  we  know  the  diameter  of  the  wheel  and  the 
pressure  against  which  the  air  is  to  be  delivered  we 
find  C,  the  capacity,  from  Table  II.  if  r  is  0.707 
or  from  Table  HA  if  r  is  0.625.  Then  knowing  C, 
P,  and  r  we  find  the  horse  power  expended  on  the 
air  by  (55). 

EXAMPLE: — Determine  the  horse  power  re- 
quired to  move  the  air  delivered  by  a  fan  for  which 
r  is  0.625  and  whose  wheel  is  8  feet  in  diameter, 
when  working  at  its  capacity  against  0.6  of  an 
ounce  per  square  inch. 

From  Table  HA  we  see  that  the  capacity  of 
an  8-foot  wheel  working  against  0.6  of  an  ounce 
is  27200  cubic  feet  per  minute.  Hence  we  have 
that  C  is  27200;  P  is  0.6;  and  since  r  is  0.625, 


WORK.  103 

1  +  r2  is   1.39.     Therefore  from   (55)  we  get  that 
the  horse  power  expended  on  the  air  is 


3670 
27200xO.6xl.39 


3670 


6.18 


If  we  do  not  know  P,  but  do  know  the  number 
of  revolutions  the  wheel  makes  per  minute  we 
must  find  P  from  Table  VI.,  then  find  C  from  either 
Table  II.  or  Table  HA,  and  then  proceed  as  before. 

EXAMPLE  : — Determine  the  horse  power  required 
to  move  the  air  by  a  fan  for  which  r  is  0.707,  and 
whose  wheel  is  7  feet  in  diameter  and  is  making 
150  revolutions  per  minute.  The  outlet  is  sup- 
posed to  be  equal  to  the  blast  area. 

From  Table  VI.  we  see  that  a  7-foot  wheel 
making  149  revolutions  per  minute  gives  a  pres- 
sure of  0.4  of  an  ounce  per  square  inch.  Hence 
P  is  0.4. 

From  Table  II.  we  see  that  for  a  7-foot  wheel 
working  against  0.4  of  an  ounce  pressure,  C  is 
24800. 

And  since  r  is  0.707,  r2  is  0,5  and  1  -|-r2  is  1.5, 

Hence 


104  CENTRIFUGAL    FANS 

3670 

24800x0.4x1.5 
3670 

«  4.06 

When  the  outlet  area  is  less  than  the  blast  area 
the  quantity  of  air  discharged  is  less  than  the 
capacity,  C,  and  is  what  we  have  called  Ct.  And 
since  the  quantity  of  air  discharged  by  the  fan  is 
less  than  C,  the  velocity  of  the  air  through  the 
inlet  is  less  than  n  r  D  N  and  the  pressure  corre- 

/7T  r  DN\2 
spending  to  this  velocity  is  less  than     (  —  j 

\       O^vJU      / 

From  (30)  we  know  that  when  a  is  the  area 
of  the  outlet  in  square  feet,  c  its  coefficient  of 
discharge,  and  A  the  blast  area,  the  expression 
for  C\,  is 

ac  C 


The  velocity  through  the  inlet  is  directly  pro- 
portioned to  the  quantity  of  air  passing  through 
it,  so  that  when  the  quantity  of  air  passing  through 
the  fan  is  C\,  the  velocity  through  the  inlet  is 


WORK.  105 

a  c  n  r  D  N 

-  2  -  .      And  the  pressure  corresponding  to 


this  velocity  is 

/a  c  it  r  D  N' 


V  =  (D  N\  a*  °2  r* 
I   :=  V1650/       A* 


\       5200 

P  a2  c2  r2 
A2 

Therefore,  the  work  done  on  the  air  alone 
when  the  theoretical  area  of  the  outlet  is  less  than 
the  blast  area  is  equal  to  9  times  the  quantity  of 
air  discharged  per  minute  multiplied  by  the  sum 

p  a2  C2  r2 

of   P    and    the    pressure    :   —^  —       which     corre- 

J\ 

sponds  to  the  velocity  at  the  inlet.  And  this 
work  divided  by  33000,  is  the  horse  power  ex- 
pended on  the  air  when  a  c  is  less  than  the  blast 
area  A.  Calling  this  work  K^  we  have 


1  " 


33000 


(56)  3670 


Inasmuch  as  we  seldom  care  to  know  the  horse 


106  CENTRIFUGAL    FANS. 

power  necessary  to  move  the  air  when  the  theo- 
retical outlet  area  is  less  than  the  blast  area  it 
is  not  necessary  to  discuss  (56).  In  actual  prac- 
tice we  are  seldom  bothered  about  the  horse  power 
required  to  move  the  air  unless  the  fan  is  working 
up  to  its  capacity,  because  upon  this  work  depends 
the  size  of  the  motor  or  engine  which  must  be  in- 
stalled to  run  the  fan. 

When  the  theoretical  outlet  area  is  greater  than 
the  blast  area  the  quantity  of  air  discharged  per 
minute  is  C2\  the  pressure  in  ounces  per  square 
inch  in  the  housing  is  p\  and  the  pressure  in 
ounces  per  square  inch  corresponding  to  the  velo- 
city through  the  inlet  is  pv  Hence  the  work 
done  on  the  air  is  9  C2  (p  +  p^ 

But  from  (31)  we  have 


P  = 
and,  therefore, 

P  +  Pi  - 


As  has  been  shown  before,  P  +  p2  is  equal  to 
P  (1-fr2).  Hence  the  work  done  on  the  air  is 
9  C2  P  (1  +r2)  and  the  horse  power,  K2,  exerted  on 
the  air  is 


(57)  Kt-  -      2330Q() 


C2P 


WORK.  107 

C^P  (1+r2) 


3670 


The  expression  for  K2  is  very  similar  to  the 
expression  for  K,  the  horse  power  when  the  fan 
is  working  at  its  capacity;  the  only  difference 
being  that  in  the  expression  for  K  we  use  C,  while 
in  the  expression  for  K2  we  use  C2.  If  we  divide 
(57)  by  (55)  and  solve  for  K 2  we  get 


(58)  K2  = 


C 


From  (39)  we  find  that  C2  =  B  C,  and  there- 
fore (58)  becomes 

(59)  K2  =  B  K 

B,  as  has  been  explained  before,  depends  upon 
the  ratio,  r,  of  the  diameter  of  the  inlet  to  the 
diameter  of  the  wheel,  and  the  ratio  of  the  theo- 
retical outlet  area,  a  c,  to  the  blast  area  A.  Values 
of  B  are  given  in  Table  IV, 


CHAPTER  VII. 


Horse  Power  Required  to  Run   a  Fan.     The 

horse  power  required  to  run  a  fan  is  the  sum  of 
the  horse  power  required  to  move  the  air  and  the 
horse  power  required  to  overcome  the  resistance 
to  the  wheel  as  it  revolves  in  the  housing.  The 
resistance  to  the  wheel  as  it  revolves  is  made  up 
of  the  friction  of  the  shaft  in  the  bearings  and  of 
the  friction  of  revolution  due  to  the  air  between 
the  wheel  and  the  housing.  It  is  extremely  diffi- 
cult to  determine  the  resistance  to  the  wheel  as  it 
revolves,  as  it  depends  upon  the  bearings,  and  upon 
the  fit  of  the  wheel  in  the  housing,  and  upon  the 
size  and  weight  of  the  shaft  and  wheel;  and  it  is 
usually  for  each  fan  a  constant  per  revolution  of 
the  wheel.  That  is  the  resistance  at  100  revolu- 
tions per  minute  of  the  wheel  is  usually  about 
twice  what  it  is  at  50  revolutions.  It  is  probably 
safe,  and  near  enough  to  the  actual  truth  for  all 
practical  purposes,  to  say  that  the  horse  power 

108 


HORSE    POWER    REQUIRED.  109 

required  to  overcome  the  resistance  to  the  turning 
of  the  wheel  is  about  10  per  cent,  of  the  total 
power  required  to  run  the  fan  when  it  is  working 
at  its  .capacity  or  above.  This  means  that  the 
mechanical  efficiency  of  the  fan  is  about  90  per  cent, 
and  that  K  as  given  by  (55)  is  0.9  of  the  total 
horse  power  required  to  run  the  fan  when  it  is 
working  at  .its  capacity. 

If  we  call  H  the  horse  power  required  to  run  a 
fan  when  its  theoretical  outlet  area  is  equal  to  the 
blast  area,  that  is  when  the  fan  is  working  at  its 
capacity,  we  have 


K 


This  equation  has  been  used  to  calculate 
Tables  VIII.  and  VIIlA. 

Table  VIII.  gives  the  horse  power  required  to 
run  a  fan  when  working  at  its  capacity  under 
different  pressures,  when  the  diameter  of  the 
inlet  is  0.707  the  diameter  of  the  wheel,  or  when 
r  is  0.707. 

Table  VI II A  gives  the  horse  power  required  to 
run  a  fan  when  working  at  its  capacity  under 
different  pressures,  when  the  diameter  of  the  inlet 
is  0.625  the  diameter  of  the  wheel,  or  when  r  is 
0.625. 


CENTRIFUGAL    FANS. 


TABLE  VIII. 

Horse  power  required  for  centrifugal  fans. 


Diam. 
of  wheel 
in  feet. 

Pressure  in  ounces  per  square  inch. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

<J.9 

1.0 

3 

0.10 

0.29 

0.54 

0.83 

1.16 

1.52 

1.92 

2.34 

2.80 

3.28 

*i 

0.14 

0.40 

0.73 

1.13 

1.58 

2.07 

2.61 

3.18 

3.81 

4  .  45 

4 

0.18 

0.52 

0.96 

1.47 

2.06 

2.72 

3.40 

4.14 

4.95 

5.82 

4* 

0.23 

0.66 

1.21 

1.85 

2.62 

3.41 

4.33 

5.27 

6.31 

7.36 

5 

0.29 

0.81 

1.50 

2.31 

3.20 

4.23 

5.32 

*6.51 

7.77 

9.10 

5J 

0.35 

0.98 

1.80 

2.78 

3.89 

5.10 

6.43 

7.85 

9.42 

11.0 

6 

0.41 

1.17 

2.16 

3.31 

4.64 

6.08 

7.67 

9.38 

11.2 

13.1 

6i 

0.49 

1.37 

2.53 

3.89 

5.43 

7.15 

9.01 

11.0 

13.2 

15.4 

7 

0.56 

1.59 

2.93 

4.51 

6.30 

8.30 

10.4 

12.7 

15.2 

17.8 

8 

0.74 

2.08 

3.82 

5.89 

8.32 

10.8 

13.6 

16.7 

19.9 

23.3 

9 

0.93 

2.64 

4.82 

7.46 

10.4 

13.7 

17.3 

21.1 

25.2 

29.5 

10 

1.15 

3.26 

5.97 

9.20 

12.9 

16.9 

21.3 

26.0 

31.1 

36.4 

11 

1.39 

3.94 

7.23 

11.1 

15.5 

20.5 

25.8 

31.5 

37.6 

44.0 

12 

1.66 

4.70 

8.62 

13.3 

18.5 

24.4 

30.7 

36.6 

44.6 

52.3 

TABLE  VIIlA. 


Pressure  in  ounces  per  square  inch. 


Ul     WilCCl 

in  feet. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

3 

0.07 

0.19 

0.34 

0.53 

0.74 

0.97 

1.22 

1.49 

1.76 

2.09 

3* 

0.09 

0.25 

0.47 

0.72 

1.00 

1.32 

1.66 

2.04 

2.43 

2.84 

4 

0.12 

0.33 

0.61 

0.94 

1.32 

1.73 

2.17 

2.64 

3.16 

3.72 

4* 

0.15 

0.42 

0.77 

1.19 

1.67 

2.18 

2.76 

3.36 

4.03 

4.68 

\     5 

0.18 

0.52 

0.96 

1.47 

2.04 

2.70 

3.39 

4.15 

4.97 

5.78 

5* 

0.22 

0.63 

1.15 

1.77 

2.49 

3.26 

4.10 

4.99 

6.00 

7.00 

6 

0.26 

0.75 

1.38 

2.11 

2.95 

3.87 

4.90 

5.97 

7.14 

8.35 

6* 

0.31 

0.88 

1.61 

2.48 

3.46 

4.55 

5.75 

7.03 

8.38 

9.78 

7 

0.36 

1.01 

1.87 

2.87 

4.01 

5.28 

6.64 

8.13 

9.72 

11.3 

8 

0.47 

1.33 

2.44 

3.76 

5.25 

6.88 

8.68 

10.6 

12.7 

14.9 

9 

0.59 

1.68 

3.08 

4.76 

6.65 

8.75 

11.0 

13.5 

16.1 

18.8 

10 

0.73 

2.08 

3.82 

5.88 

8.21 

10.8 

13.6 

16.6 

19.8 

23.2 

11 

0.89 

2.52 

4.61 

7.10 

9.90 

13.1 

16.5 

20.1 

24.0 

28.1 

12 

1.06 

3.00 

5.51 

8.48 

11.8 

15.5 

19.6 

23.3 

28.5 

33.4 

HORSE    POWER    REQUIRED.  Ill 

When  the  theoretical  outlet  area  is  less  than  the 
blast  area,  that  is  when  a  c  is  less  than  A,  the 
horse  power  required  to  run  the  fan  is  equal  to  the 
horse  power  Kiy  required  to  move  the  air,  as  given 
by  (56),  plus  the  horse  power  required  to  over- 
come the  resistance  to  turning  the  wheel.  If  we 
assume  the  resistance  to  turning  the  wheel  to  be 
10  per  cent,  of  the  horse  power  required  to  run 
the  fan  when  working  at  its  capacity,  or  0.1  of 
H  as  given  by  (60),  the  horse  power,  H±,  required 
to  run  the  fan  will  be 


(61) 


When  the  theoretical  outlet  area  is  greater  than 
the  blast  area,  that  is  when  a  c  is  greater  than  A, 
the  horse  power,  which  we  may  call  H2,  required  to 
run  the  fan  will  be  the  horse  power  K2,  as  given 
by  (59),  required  to  move  the  air  plus  the  horse 
power  required  to  overcome  the  resistance  to  turn- 
ing of  the  wheel.  We  are  probably  safe  in  assuming 
here,  as  before,  that  the  mechanical  efficiency  of 
the  fan  is  about  90,  or  that  K2  is  about  0.9  of  H2. 
Hence  from  (59)  we  have 


112  CENTRIFUGAL    FANS. 

(62)  "'  =  £1=^ 

But  from   (60)  we  know  that 
—       H 

and  therefore  (62)  becomes 

C  P  (1  +  i 


(63) 


The  value  of  #  for  a  wheel  whose  inlet  has  a 
diameter  equal  to  0.707  or  0.625  of  the  diameter 
of  the  wheel,  may  be  obtained  from  Table  VIII. 
or  Table  VIII A,  and  the  value  of  B  for  various 
ratio  of  theoretical  area  of  outlet  to  blast  area 
may  be  obtained  from  Table  IV. 

EXAMPLE  : — Determine  the  horse  power  required 
to  run  a  fan  whose  inlet  is  37^  inches  in  diameter,  and 
whose  wheel  is  5  feet  in  diameter,  when  running  at 
275  revolutions  per  minute  with  a  theoretical  out- 
let area  equal  to  the  blast  area;  and,  also,  when  the 
theoretical  outlet  area  is  1.4  the  blast  area. 

Here  we  have  that  r,  the  ratio  of  the  diameter 
of  the  inlet  to  the  diameter  of  the  wheel,  is 


37'6      0.625 


60 


i 


HORSE    POWER    REQUIRED..  113 

From  Table  VI.  we  find  that  when  a  5-foot 
wheel  is  making  275  (exactly  276  in  the  Table) 
revolutions  per  minute  the  pressure  against  which 
it  is  working,  when  the  outlet  is  equal  to  the 
blast  area,  is  0.7  of  an  ounce  per  square  inch. 

And  from  Table  VIIlA  we  find  that  a  fan  with  a 
5-foot  wheel  working  at  its  capacity  against  a 
pressure  of  0.7  of  an  ounce,  requires  3.4  horse 
power  to  run  it. 

When  the  theoretical  outlet  area  is  made  1.4 
the  blast  area  we  find  from  Table  IV.  that  for  r 
equal  to  0.625,  B  is  1.24.  We  have  just  found 
that  H  is  3.4.  Hence  the  horse  power  H2,  required 
to  run  the  fan  when  the  theoretical  outlet  area 
is  1.4  the  blast  area  is  from  (63) 

H2  =  B  H 

1.24x3.4 

=  4.2 

It  is  interesting  to  look  into  the  performance 
of  this  fan  as  to  delivering  air  under  the  two 
conditions  of  outlet  openings. 

From  Table  HA  we  see  that  a  5-foot  wheel 
working  at  its  capacity  under  a  pressure  of  0.7 
of  an  ounce,  delivers  16,700  cubic  feet  of  air  per 
minute.  When  the  theoretical  area  of  the  outlet 
is  greater  than  the  blast  area,  we  know  from  (39) 


114  CENTRIFUGAL    FANS. 

that  the  quantity  of  air  delivered,  C2,  is  B  times 
the  capacity  as  given  by  Table  HA.     And  from 

Table  IV.  we  find  that  when—  is    1.4,   as    in    the 

J\ 

example,  B  is  1.24  for  r  equal  0.625.     Therefore, 
in  this  case 

C2  =  B  C  =--  1.24x16700 
=  20700 

We  also  know  that  when  the  theoretical  outlet 
area  is  1.4  the  blast  area,  the  pressure  in  the  hous- 
ing at  the  outlet  is,  from  (54),  equal  to  F  P.  In 
this  case  P  is  0.7  of  an  ounce  per  square  inch,  and 
F,  from  Table  VII.  for  r  equal  0.625,  is  0.79. 

Hence 

p  =  FP  =  0.79x0.7 

=  0.55 

Therefore  when  the  theoretical  outlet  area  is 
equal  to  the  blast  area,  we  find  that  for  this  fan 
making  275  revolutions  per  minute,  the  pressure 
in  the  housing  is  0.7  ounces  per  square  inch; 
the  cubic  feet  of  air  delivered  per  minute  is 
16700;  the  horse  power  required  to  run  the  fan 
is  3.4. 

When  the  theoretical  outlet  area  is  1.4  the  blast 
area  we  find  that,  the  pressure  in  the  housing  is 
0.55  ounces  per  square  inch;  the  cubic  feet  of  air 


ENGINE    REQUIRED.  115 

delivered  per  minute  is  20700;    the  horse  power 
required  to  run  the  fan  is  4.2. 

Engine  Required  to  Run  a  Fan.  The  horse 
power  of  the  engine  required  for  a  fan  is  equal  to 
the  horse  power  required  to  run  the  fan  divided 
by  the  efficiency  of  the  engine.  The  efficiency  of 
engines  used  to  run  fans  is  usually  between  f  and  £ 
for  engines  belted  to  the  fans  and  between  J  and  f 
for  those  direct  connected  to  the  fans.  If  we  call 
the  horse  power  of  the  engine  E  and  assume  that 
the  efficiency  is  |,  a  fairly  good  average  value,  we 
have  from  (60)  that  the  engine  required  to  run  a 
fan  when  working  at  its  capacity  is 


/A/n  IT 

(64)  E  = 


In  the  same  way  if  we  call  E2  the  horse  power 
of  the  engine  required  to  run  a  fan  when  the  theo- 
retical area  of  the  outlet  is  greater  than  the  blast 
area,  we  find  from  (63)  that 


CP  (l  +  r' 
2200 


116  CENTRIFUGAL    FANS. 

When  choosing  an  engine  to  run  a  fan  it  will 
usually  be  sufficient  to  choose  one  to  run  the  fan 
when  working  at  its  capacity ;  and  if  proper  care  be 
used  to  see  that  the  engine  chosen  is  not  too  small 
to  easily  run  the  fan  when  working  at  its  capacity, 
it  will  usually  be  large  enough  to  run  the  fan  when 
the  outlet  area  is  somewhat  greater  than  the  blast 
area.  This  method  of  chosing  an  engine  to  run  a 
fan  is  a  safe  one  in  view  of  the  fact  that  a  fan  is 
usually  chosen  of  such  a  size  that  it  will  deliver 
the  required  quantity  of  air  against  a  given  pres- 
sure when  working  at  its  capacity.  It  is  not 
necessary  to  bother  about  the  size  of  engine  re- 
quired to  run  a  fan  when  its  theoretical  outlet  area 
is  less  than  the  blast  area,  since  if  the  engine  is 
large  enough  to  run  the  fan  at  its  capacity  there 
will  be  no  trouble  when  the  fan  is  working  at  less 
than  its  capacity. 

When  the  engine  is  belted  to  the  fan  or  the  fan 
is  "  belt  connected  "  the  problem  of  selecting  the 
engine  resolves  itself  into  merely  selecting  that 
engine  which  will  give  the  desired  horse  power 
when  using  steam  at  the  pressure  to  be  carried  in 
the  boiler.  In  this  case  the  speed  at  which  the 
engine  is  to  run  is  a  matter  of  no  consequence,  as 
whatever  this  speed  may  be  the  speed  of  the  fan 
may  be  made  anything  desired  by  choosing  the 
pulleys  on  the  fan  and  engine  of  the  proper  sizes. 
When,  however,  the  fan  and  engine  are  mounted 
on  the  same  shaft  or  the  fan  is  "  direct  connected," 


ENGINE   REQUIRED.  117 

the  problem  becomes  somewhat  more  difficult  as  the 
matter  of  torque  or  turning  effort  of  the  engine 
enters  very  largely.  If  a  fan  is  direct  connected 
to  an  engine,  when  steam  is  turned  on  and  the 
engine  started,  the  engine  will  speed  up  gradually 
and  since  the  work  done  by  the  fan  will  gradually 
increase  as  the  speed  increased  there  will  soon  be 
reached  a  speed  which  is  the  maximum  possible 
for  the  engine  with  the  given  conditions  of  steam 
pressure,  cut-off,  and  back  pressure. 

If  in  (60)  we  make  r  equal  to  0.707  we  get  that 
the  power  required  to  run  a  fan  whose  ratio  of 
diameter  of  inlet  to  diameter  of  wheel  is  0.707, 
when  working  at  its  capacity,  is 


H- 


From  the  well-known  formulas  in  regard  to 
steam  engines*  we  know  that  the  indicated  horse 
power  developed  by  a  double  acting  engine  whose 
length  of  stroke  is  /  inches  and  whose  diameter  of 
cylinder  is  d  inches,  when  making  N  revolutions 
minute  and  using  steam  whose  mean  effective 
pressure  is  Pf  pounds  per  square  inch,  is 

2P'lxd2N        P'ld2N 


12x4x33000         251000 


*See  Steam  Engines  and    Boilers,  bv  I.  H.  Kinealv. 


118  CENTRIFUGAL    FANS. 

Now  let  y  be  the  efficiency  of  the  engine,  then 
the  indicated  horse  power  of  the  engine  multiplied 
by  y  must  equal  the  horse  power  required  to  run 
the  fan.  That  is  to  sa 


251000 

And  from  (66)  we  get 

CP  yP' 


(68) 


2200  251000 


From  (15)  we  get  by  making  r  equal  0.707, 
C  =  0.49  D*  N 

where  as  before  D  is  the  diameter  of  the  fan  wheel 
in  feet  and  N  is  the  number  of  revolutions  per 
minute  at  which  it  is  run. 

This  value  of  C  in  (68)  gives, 

UM  0.49  £3P        yP'ld? 

2200  251000 

From  this  we  get 
(70)  /*- 


ENGINE   REQUIRED.  119 

y  is  seldom  greater  than  f  and  it  may  often  be 
only  \.  In  the  case  of  an  engine  run  by  steam 
under  20  pounds  by  the  gauge  it  is  best  to  assume 
that  y  is  \.  Then  (70)  becomes 


„,, 


Direct  connected  engines  seldom,  have  gov- 
ernors, and  they  are  usually  of  the  throttling  type 
and  arranged  to  cut-off  at  about  f  or  f  the  stroke. 
When  the  exhaust  from  the  engine  is  not  used  for 
heating  purposes  so  that  there  is  no  unusual  back 
pressure  on  the  engine  we  may  say  that  the  mean 
effective  pressure  Pr  of  the  steam  in  the  engine 
is  equal  to  0.9  the  boiler  pressure,  less  2.  That 
is,  if  P"  is  the  boiler  pressure  and  the  exhaust  steam 
is  not  used  for  heating  purposes, 

P'  =  0.9  P"- 2 

If  the  exhaust  steam  is  used  for  heating  pur- 
poses there  will  usually  be  a  back  pressure  of  about 
2  pounds  and  then 

P'  =  0.9  P'7- 4 

Table  IX.  gives  the  mean  effective  pressure 
which  may  be  expected  in  ordinary  direct  con- 
nected engines  for  different  boiler  pressures. 


120 


CENTRIFUGAL    FANS. 

TABLE  IX. 
Mean  effective  pressures. 


Boiler 

Mean  effective  pressure  when  the 

pressure 

exhaust  is 

in  pounds. 

not  used  for  heating. 

used  for  heating. 

10 

7.0 

5.0 

15 

11.5 

9.5 

20 

16.0 

14.0 

25 

20.5 

16.5 

30 

25.0 

23.0 

40 

34.0 

32.0 

50 

43.0 

41.0 

75 

65.5 

63.5 

100 

88.0 

86.0 

In  the  case  of  engines  used  with  low  pressure 
heating  plants  where  the  boiler  pressure  is  about 
15  pounds  it  is  usually  safe  to  say  that  when  the  ex- 
haust steam  is  not  used  for  heating  purposes 

/  d2  =  10  D3  P 

And  when  the  exhaust  steam  is  used  for  heat- 
ing purposes 

/  d2  =  12D3P 

EXAMPLE: — What  should  be  the  size  of  engine 
direct  connected  to  a  fan  having  a  6^-foot  wheel 
in  order  to  run  it  at  a  ^  ounce  pressure  with  steam 
in  the  boiler  at  15  Ibs.,  if  the  exhaust  is  used  for 
heating  ? 

Table  IX.  shows  that  the  mean  effective  pres- 


ENGINE    REQUIRED.  121 

sure  is  9.5  when  the  exhaust  is  used  for  heating 
and  the  boiler  pressure  is  15. 

And   since   P   is    £   by   the    conditions    of   the 
problem,  we  have  from   (71) 


Now  we  must  choose  from  the  catalogue  list  of 
sizes  of  the  engine  we  desire  to  use  one  whose 
length  of  stroke  in  inches  multiplied  by  the  square 
of  the  diameter  of  the  cylinder  in  inches  will  be 
equal  to  1740. 

In  this  particular  case  if  /  equal  14  and  d 
equal  11,  we  have 

Id2  =  14x121  =  1694 

Hence  an  11  by  14  engine  would  be  the  proper 
one  to  use. 


Motor  Required  to  Run  a  Fan.  Electric  motors 
are  usually  supposed  to  be  rated  according  to 
the  power  they  will  deliver  on  their  own  pulleys, 
which  means  that  the  horse  power  of  the  motor  re- 
quired for  a  fan  would  be  the  same  as  the  horse  power 


122  CENTRIFUGAL    FANS. 

required  to  run  the  fan  plus  the  slight  loss  between 
the  fan  and  the  motor.  To  make  this  assumption, 
however,  when  choosing  a  motor  for  a  fan  would 
mean  "  figuring  "  closer  than  can  be  considered 
good  engineering.  The  writer  usually  assumes  that 
the  efficiency  of  transmission  between  the  motor 
and  the  fan  is  about  75  per  cent.,  which  makes  the 
horse  power  of  the  motor  equal  the  horse  power 
required  to  run  the  fan  divided  by  0.75.  On  this 
assumption  the  horse  power  of  the  motor,  which 
we  may  call  M  for  a  fan  working  at  its  capacity  is 
from  (60) 


CP  (1  +  r2) 
2450 

In  the  same  way  the  horse  power,  M2,  of  the 
motor  for  a  fan  when  its  theoretical  outlet  area  is 
greater  than  the  blast  area  is  from  (62) 

(73)  M2  -  -^  -  1** 

CP  ( 
2450 


MOTOR    REQUIRED.  123 

The  same  remarks  in  regard  to  choosing  an 
engine  for  a  fan,  apply  to  choosing  a  motor.  It  is 
much  better  to  have  the  motor  too  large  than  too 
small,  and  when  there  is  any  doubt  as  to  the  power 
required  to  run  the  fan  it  is  well  to  err  on  the  side 
of  safety  and  choose  a  motor  of  such  a  size  that  it 
can  easily  run  the  fan.  Another  reason  for  choos- 
ing a  motor  or  engine  of  liberal  size  for  a  fan  is  that 
it  often  happens  that  for  one  reason  or  another  it 
becomes  necessary  to  speed  up  the  fan,  thus  in- 
creasing the  pressure  against  which  it  works  or  the 
quantity  of  air  delivered  per  minute  or  both.  And 
each  one  of  these  increases  results  in  an  increase 
in  the  horse  power  required  to  run  the  fan,  and 
hence  an  increased  demand  on  the  motor  or  engine. 

If  the  motor  is  direct  connected  to  the  fan  it 
will,  of  course,  have  to  run  at  the  same  speed  as 
the  fan  and  this  will  usually  result  in  necessitating 
a  motor  of  much  larger  size  than  would  be  required 
if  the  motor  were  belted  to  the  fan.  If  the  speed 
of  a  motor  be  decreased  and  made  less  than  its 
normal  speed  or  less  than  the  speed  for  which  the 
motor  was  originally  designed,  the  power  developed 
by  the  motor  will  be  decreased  in  almost  the  same 
ratio  as  the  speed.  That  is  to  say  if  a  10  horse 
power  motor  be  designed  to  run  at  800  revolutions 
a  minute  and  it  be  desired  that  this  motor  be  run 
at  200  revolutions  instead  of  800  then  the  motor 
instead  of  developing  10  horse  power  would  de- 
velope  about  one-fourth  of  10  horse  power  or  2^ 


124  CENTRIFUGAL    FANS. 

horse  power.  When  motors  are  direct  connected 
to  fans  they  are  usually  obliged  to  run  at  much  less 
speed  than  if  they  are  belted  and  hence  because 
of  the  larger  size  motor  required  a  direct  connected 
motor  is  much  more  expensive  for  a  fan  than  a 
belted  motor.  Thus,  if  a  fan  requires  8  horse 
power  to  drive  it  at.  160  revolutions  a  minute  which 
is  about  one-fifth  of  the  speed  at  which  a  8  horse 
power  would  ordinarily  be  expected  to  run,  it  would 
be  necessary  to  get  what  would  at  an  ordinary 
speed  of  about  800  revolutions  a  minute  be  a  40 
horse  power  motor.  That  is  because  the  speed 
of  the  motor  is  only  about  one-fifth  that  at  which 
it  would  ordinarily  be  run,  it  would  be  necessary 
to  get  a  motor  about  5  times  as  large.  This  motor 
would  not  develop  40  horse  power  at  160  revolu- 
tions but  would  develop  about  8  horse  power  and 
the  cost  of  the  motor  would  be  pretty  nearly  the 
same  as  the  ordinary  40  horse  power  motor. 

A  direct  connected  motor  for  a  fan  may  usually 
be  expected  to  cost  from  4  to  6  times  as  much  as  a 
belted  motor. 


Width  of  Belt.  As  a  matter  of  convenience  in 
determining  the  size  or  width  of  a  leather  belt  re- 
quired to  drive  a  fan,  Tables  X  and  XA  have  been 
calculated. 

Table  X  is  for  single  thick  belts,  and  is  based 
upon  the  supposition  that  one  inch  of  width  of  belt 


BELT. 


TABLE  X. 

Horse  power  transmitted  by  single  belts. 


Width 

Speed  of  belt  in  feet  per  minute. 

of  belt 
in  in. 

500 

1000 

1500 

2000 

2500 

3000 

3500 

4000 

4500 

5000 

2 

1.3 

2.5 

3.8 

5.0 

6.3 

7.5 

8.8 

10.0 

11.2 

12.5 

?* 

1.6 

3.1 

4.7 

6.3 

7.8 

9.4 

11.0 

12.5 

14.1 

15.  6a 

3 

1.9 

3.8 

5.6 

7.5 

9.4 

11.2 

13.1 

15.0 

16.9 

18.8 

4 

2.5 

5.0 

7.5 

10.0 

12.5 

15.0 

17.5 

20.0 

22.5 

25.0 

5 

3.1 

6.3 

9.4 

12.5 

15.6 

18.8 

21.9 

25.0 

28.1 

31.3 

6 

3.8 

7.5 

11.2 

15.0 

18.8 

22.5 

26.2 

30.0 

33.8 

37.5 

7 

4.4 

8.8 

13.1 

17.5 

21.9 

26.3 

30.6 

35.0 

39.4 

43.8 

8 

5.0 

10.0 

15.0 

20.0 

25.0 

30.0 

35.0 

40.0 

45.0 

50.0 

9 

5.6 

11.2 

16.9 

22.5 

28.1 

33.7 

39.3 

45.0 

50.6 

10 

6.3 

12.5 

18.8 

25.0 

31.2 

37.5 

43.7 

50.0 

TABLE  XA. 

Horse  power  transmitted  by  double  belts. 


Width 

Speed  of  belt  in  feet  per  minute. 

of  belt 
in  in. 

500 

1000 

1500 

2000 

2500 

3000 

3500 

4000 

4500 

5000 

2 

1.8 

3.6 

5.5 

7.3 

9.1 

10.9 

12.7 

14.5 

16.4 

18.2 

2* 

2.3 

4.5 

6.8 

9.1 

11.4 

13.6 

15.9 

18.2 

20.5 

22.8 

3 

2.7 

5.5 

8.2 

10.9 

13.6 

16.4 

19.1 

21.8 

24.6 

27.3 

4 

3.6 

7.3 

10.9 

14.5 

18.2 

21.8 

25.4 

29.1 

32.7 

36.4 

5 

4.5 

9.1 

13.6 

18.2 

22.7 

27.3 

31.8 

36.4 

40.9 

45.5 

6 

5.5 

10.9 

16.3 

21.8 

27.2 

32.7 

38.2 

43.6 

49.1 

7 

6.4 

12.7 

19.1 

25.4 

31.8 

38.2 

44.5 

50.9 

8 

7.3 

14.5 

21.8 

29.1 

36.3 

43.6 

50.9 

9 

8.2 

16.4 

24.5 

32.7 

40.9 

49.1 

10 

9.1 

18.2 

27.2 

36.3 

45.4 

54.5 

126  CENTRIFUGAL    FANS. 

will  transmit  one  horse  power  when  travelling  at  a 
speed  of  800  feet  per  minute. 

Table  XA  is  for  double  thick  belts,  and  is  based 
upon  the  supposition  that  one  inch  of  width  of  belt 
will  transmit  one  horse  power  when  travelling  at  a 
speed  of  550  feet  per  minute. 

To  use  either  table  X  or  X A  it  is  necessary  to 
know  the  speed  of  the  belt  in  feet  per  minute,  and 
this  is  obtained  by  multiplying  the  circumference 
of  the  pulley  on  which  the  belt  runs  by  the  number 
of  revolutions  it  makes  per  minute.  The  circum- 
ference must  be  in  feet,  and  is  always  equal  to  n 
times  the  diameter  in  feet.  But  it  is  usual  to  ex- 
press the  sizes  or  diameters  of  pulleys  in  inches,  and 
hence  the  diameter  in  feet  will  be  equal  to  the  size 
or  diameter  in  inches  divided  by  12.  Therefore, 
if  d  is  the  diameter  of  the  pulley  in  inches,  the  cir- 
cumference in  feet  will  be 


12  12 


=  3.82 

For  all  practical  purposes  connected  with  the 
calculation  of  belts  it  is  sufficiently  exact  to  say 
that  the  circumference  of  a  pulley  in  feet  is  equal 
to  one-fourth  of  the  diameter  of  the  pulley  in  in- 


BELT.  127 

ches.  And  hence  the  speed  of  the  belt  used  to 
drive  a  fan  is  equal  to  one-fourth  the  product  of 
the  diameter  of  the  pulley  on  the  fan,  in  inches, 
multiplied  by  the  number  of  revolutions  it  makes 
per  minute. 

EXAMPLE: — Determine  the  width  of  a  single 
belt  running  on  a  pulley  40  inches  in  diameter  and 
making  200  revolutions  per  minute  necessary  to 
transmit  11  horse  power. 

Here,  since  the  diameter  of  the  pulley  in  inches 
is  40  and  the  number  of  revolutions  per  minute  is 
200,  the  speed  of  the  belt  in  feet  per  minute  is 


40*200=2000 


Looking  now  in  Table  X,  since  the  belt  is  to  be 
a  "'  single  "  belt,  we  find  under  the  column  headed 
2000,  that  a  belt  four  inches  wide  will  transmit  10 
horse  power  and  a  belt  5  inches  wide  will  transmit 
12.5  horse  power.  We  may,  therefore,  use  a  4  inch 
belt  at  about  10  per  cent,  above  its  capacity  or 
we  may  use  a  5  inch  belt  at  about  80  per  cent,  of  its 
capacity.  In  most  cases  it  would  probably  be  best 
to  use  the  5  inch  belt. 

From  Table  XA  we  see  that  a  3  inch  double 
belt  will  transmit  10.9  horse  power  when  running 
at  a  speecl  of  2000  feet  per  minute. 


CHAPTER  VIII 


Efficiency.  The  efficiency  of  a  fan  may  mean 
either  of  two  things;  it  may  mean  the  quotient 
obtained  by  dividing  the  useful  work  by  the  work 
done  on  the  air,  or  it  may  mean  the  quotient 
obtained  by  dividing  the  useful  work  by  the  work 
required  to  run  the  fan.  The  useful  work  is  the 
product  obtained  by  multiplying  the  quantity  of 
air  delivered  per  minute  by  the  pressure  in  the 
housing  at  the  outlet.  The  quantity  of  air  must 
be  expressed  in  cubic  feet  and  the  pressure  must 
be  in  pounds  per  square  foot. 

It  seems  to  the  writer  to  be  more  reasonable 
and  more  in  accordance  with  the  meaning  of  the 
word  efficiency  when  used  in  connection  with  other 
machines,  to  say  that  the  efficiency  of  a  fan  is  the 
quotient  obtained  by  dividing  the  useful  work 
by  the  work  required  to  run  the  fan ;  and  it  is  with 
this  meaning  that  the  word  will  be  used  here. 

When  the  theoretical  outlet  area  is  less  than  the 

128 


EFFICIENCY.  129 

blast  area,  the  pressure  in  ounces  per  square  inch 
in  the  housing  near  the  outlet  is  P,  the  pressure  due 
to  the  velocity  of  the  tips  of  the  floats,  and  the 
number  of  cubic  feet  of  air  discharged  per  minute 
is  C\.  As  has  been  shown  before  in  order  to  con- 
vert pressure  in  ounces  per  square  inch  into  pres- 
sure in  pounds  per  square  foot  it  is  necessary  to 
multiply  the  pressure  in  ounces  per  square  inches 
by  9.  Hence  in  this  case  the  pressure  in  pounds 
per  square  foot  is  9  P.  And  since  the  number  of 
cubic  feet  of  air  discharged  per  minute  is  Ci  the  use- 
ful work  is  9  d  P.  Divide  this  by  33000  and  we 
get  that  the  useful  horse  power  is 


33000       3670 

The  horse  power  required  to  run  the  fan  is 
equal  to  the  horse  power  expended  on  the  air  plus 
the  horse  power  required  to  overcome  the  resis- 
tance to  turning  of  the  wheel.  If  we  call  k  the  horse 
power  required  to  overcome  the  resistance  to  turn- 
ing of  the  wheel,  and  remember  that  the  horse 
power  expended  on  the  air  as  given  by  (56)  is  Klt 
we  have  the  horse  power  required  to  run  the  fan  is 
K,  +  k 

Then  the  efficiency,  which  we  may  call  elt  is  the 
useful  horse  power  divided  by  the  horse  power 
required  to  run  the  fan ;  that  is 


130  CENTRIFUGAL    FANS. 


3670  (Kl  +  k) 

Substitute  in  this  expression  the  value  of  Kl 
as  given  by  (56)  and  we  get 


(74)      et 


a2  c2  r2      3670  k 
A2  C,P 


It  must  be  remembered  that  k  is  probably  not 
exactly  the  same  for  any  two  fans.  It  depends 
upon  the  construction  and  lubrication  of  the  bear- 
ings of  the  shaft,  the  way  the  wheel  is  mounted, 
the  weight  of  the  wheel,  the  construction  of  the 
housing  and  its  fit  to  the  wheel,  and  a  great  many 
other  details  of  the  construction  of  the  fan.  If 
we  assume  as  we  did  in  (61)  that  k  is  equal  to 
0.1  of  H  as  given  by  (60)  we  have 


33000 
and 


EFFICIENCY.  131 

3670  k        3670  CP  (1+r2) 
Cl  P  33000  Cl  P 


9C, 

But  from  (30)  we  have 

iC    _  A_ 

Cl        a  c 

Hence 

3670  &        A  (1  +  r2) 


C\  P  9  a 

and  this  in  (74)  gives 
(75)          e,  =  - 


a2  c2  r2      A  (1  +  r2) 
~~ 


When  the  theoretical  area  is  equal  to  the  blast 
area,  as  it  is  when  the  fan  is  working  at  its  capa- 
city, the  efficiency,  which  we  may  call  e  in  this 
case,  becomes  from  (75) 


132 

(76) 


CENTRIFUGAL    FANS. 

1 


1  + 


1-fr2 


0.9 

1  +  r2 


It  will  be  noticed  that  (76)  shows  that  the 
efficiency  of  a  fan  working  at  its  capacity  depends 
only  upon  r,  the  ratio  of  the  diameter  of  the  inlet 
to  the  diameter  of  the  wheel.  To  show  the  effect 
on  the  efficiency  of  a  variation  in  the  value  of  r, 
Table  XL  has  been  calculated  from  (76). 

TABLE  XI. 
Efficiencies. 


r 

e 

0.25 

0.85 

0.35 

0.80 

0.50 

0.72 

0.625 

0.65 

0.707 

0.60 

0.75 

0.58 

Table  XI.  shows  that  the  efficiency  of  a  fan 
whose  inlet  is  0.5  the  diameter  of  the  wheel  is 
0.72,  while  the  efficiency  of  a  fan  whose  inlet  is 
0.707  the  diameter  of  the  wheel  is  only  0.60.  In 
other  words,  the  fan  with  the  smaller  ratio  of 
inlet  to  diameter  of  wheel  is  20  per  cent,  more 


EFFICIENCY.  133 

efficient  than  the  fan  with  the  larger  ratio  of  inlet 
to  diameter.  It  is  this  difference  in  efficiency  that 
makes  it  preferable  to  use  a  fan  with  a  small  ratio 
of  inlet  to  diameter  of  wheel  when  working  against 
comparatively  high  pressures. 

Suppose  it  is  required  to  deliver  20000  cubic 
feet  of  air  per  hour  against  a  pressure  of  one  ounce 
per  square  inch.  Table  II.  shows  that  a  fan  with 
a  5-foot  wheel  with  an  inlet  0.707  the  diameter 
of  the  wheel  will  do  the  work;  and  Table  HA  shows 
that  a  fan  with  an  inlet  0.625  the  diameter  of  the 
wheel  will  require  a  6-foot  wheel.  Table  VIII. 
shows  that  the  5-foot  wheel  will  require  9.1  horse 
power  to  run  it,  while  Table  VIII A  shows  that  only 
8.4  horse  power  will  be  required  to  run  the  fan 
with  a  6-foot  wheel.  By  using  the  fan  with  a 
6-foot  wheel  a  saving  of  8  per  cent,  will  be  made 
in  the  power  required  to  run  the  fan  as  compared 
to  the  power  which  would  be  required  for  the  fan 
with  the  5-foot  wheel. 

The  diameter  of  the  inlet  of  the  fan  with  the 
5-foot  wheel  would  be  60  X  0.707  =  42.5  inches; 
while  the  diameter  of  the  inlet  of  the  fan  with  the 
6-foot  wheel  would  be  72  x  0.625  =  45  inches. 

When  the  theoretical  outlet  area  is  greater 
than  the  blast  area  the  pressure  in  ounces  per 
square  inch  in  the  housing  at  the  outlet  is  p,  and 
the  pressure  in  pounds  per  square  foot  is  9p.  Since 
the  number  of  cubic  feet  of  air  discharged  is  C2l 
the  useful  work  is  9p  C2.  But  from  (52)  we  have 


134  CENTRIFUGAL    FANS. 

P 


a2  c2  r2 
2 


and  this  value  of  p  in  the  expression  for  the  useful 
work  gives 


9 


This  divided  by  33000  gives  for  the  useful  horse 
power, 


C2P 


33000  "  3670 


From  (63)  we  find  that  the  horse  power  re- 
quired to  run  a  fan  when  its  theoretical  outlet 
area  is  larger  than  the  blast  area  is 


2 


3300 


Calling  the  efficiency  £2,  we  have 

VpC2  0.9  C2 

(77)      '*  ~  33000  H'  " 


EFFICIENCY.  135 

From  (39)  we  have  C2  =  C  B,  and  hence  (77) 
becomes 

0.9 

(78)  ^2    ~  ~2    ^    ^2 


1 


Equation  (78)  is  based  upon  the  expression 
for  H2  as  given  in  (63)  which  is  based  upon  the 
assumption  that  the  mechanical  efficiency  of  the 
fan  is  0.9.  That  is,  that  when  a  fan  is  working 
at  its  capacity  or  above  its  capacity  only  0.1  of  the 
total  power  applied  to  it  is  used  in  overcoming 
the  resistance  to  the  turning  of  the  wheel  due  to 
friction,  and  0.9  of  the  total  power  is  expended 
on  the  air. 

Equations  (76)  and  (78)  enable  us  to  compare 
the  efficiencies  of  two  fans,  one  working  at  its 
capacity  with  an  outlet  area  equal  to  the  blast 
area,  and  the  other  working  above  its  capacity 
with  an  outlet  area  greater  than  the  blast  area. 

EXAMPLE: — It  is  necessary  to  supply  30000 
cubic  feet  of  air  per  minute  against  a  pressure  of 
0.6  of  an  ounce  per  square  inch.  Determine  the 
efficiency  of  a  fan  which  will  do  this  when  working 
at  its  capacity,  and,  also,  the  efficiency  of  a  smaller 
fan  working  beyond  its  capacity  to  do  the  work. 
Assume  for  the  smaller  fan  that  the  ratio  of  the 
theoretical  outlet  area,  a  c,  to  the  blast  area,  A, 
is  1.6. 


136  CENTRIFUGAL    FANS. 

From  Table  II.  we  find  that  a  fan  with  a  7-foot 
wheel  will  deliver  30400  cubic  feet  of  air  against 
a  pressure  of  0.6  ounces  when  working  at  its  capa- 
city. 

We  know  that  when  the  theoretical  outlet 
area  is  greater  than  the  blast  area  the  pressure 
p  at  the  outlet  is  less  than  the  pressure  P  corre- 
sponding to  the  velocity  of  the  tips  of  the  floats, 
and  from  (54)  we  have 

p  =  FP 

For  —    equal    1.6   we    have   from  Table  VII. 

that  F  is  0.66  when  r  is  0.707.     We  also  know  from  ' 
the  condition  of  the  problem  that  p  is  0.6.     There- 
fore 


From  Table  IV.  we  find  that    when  — - —    is 

A 

1.6  and  r  is  0.707,  B  is  1.30.  From  (39)  we  get 
that  the  quantity  of  air  delivered  by  a  fan  when 
its  theoretical  outlet  area  is  greater  than  the  blast 
area,  is 

C,  =  C  B 


EFFICIENCY.  137 

From  this  we  get,   remembering  that  in   our 
problem  C2  is  30000 


_  23100 


1. 


Now  we  must  look  in  Table  II.  and  find  the 
diameter  of  the  wheel  whose  capacity  is  23100 
when  working  against  a  pressure  of  0.91.  The 
table  shows  that  a  fan  with'  a  5^-foot  wheel  has  a 
capacity  of  23000  cubic  feet  per  minute  against  a 
pressure  of  0.9  ounces  per  square  inch. 

From  Table  VIII.  the  horse  power  required  to 
run  the  fan  with  the  7-foot  wheel  is  8.28;  and  the 
horse  power  required  to  run  the  5^-foot  wheel 
when  working  at  its  capacity  against  0.9  of  an 
ounce  is  9.4.  But  the  5^-foot  wheel  must  be 
worked  above  its  capacity,  and  by  (63)  we  get  that 
the  horse  power  required  to  run  it  is  then 

H2  =  H  B 

H  we  have  just  found  to  be  9.4,  and  B  we 
have  found  to  be  1.3.  Therefore  the  horse  power 
required  to  run  the  5?  foot  fan  is 

H2  =  9.4x1.3 
=  12.2 


138  CENTRIFUGAL    FANS. 

The  efficiency  of  the  7-foot  fan,  for  which  r  is 
0.707,  is,  from  (76), 


0.9 

e  = 


=  0.6 


+  0.7072 


From  (78)  we  get  that  the  efficiency  of  the 
fan  with  the  5^-foot  wheel,  for  which  r  is  also 
0.707,  is 


0.9 


1-^2 


A2 


=  0.38 


1.62x0.7072 


Air  Per  Horse  Power.  It  is  sometimes  inter- 
esting to  know  the  number  of  cubic  feet  of  air, 
which  we  may  call  /,  that  a  fan  will  deliver  per 
minute  per  horse  power  applied  to  the  wheel. 

When  a  fan  is  working  at  its  capacity  we  have, 


AIR    PER    HORSE    POWER.  139 

from   (60),  that  the  air  delivered  per  minute  per 
horse  power  is 


(79)  /-' 


~  H    ~  P(l+r2) 

and  when  the  fan  is  working  beyond  its  capacity 
so  that  the  theoretical  outlet  area  is  greater  than 
the  blast  area,  the  air  delivered  per  minute  per 
horse  power  is,  from  (62), 


Cg  _    0.9 


H2  K2 

From  (57)  we  have 


3670 
and  hence  we  get  for  12 

(80)  12  = 


C2  _        3300 


Equations  (79)  and  (80)  show  that  the  air  de- 
livered per  minute  per  horse  by  a  fan  depends 
upon  the  pressure,  P,  corresponding  to  the  tips  of 


140  CENTRIFUGAL    FANS. 

the  floats  and  the  ratio,  r,  of  the  diameter  of  the 
inlet  to  the  diameter  of  the  wheel.  The  equations 
further  show  that  for  given  values  of  P  and  r,  the 
air  delivered  per  minute  per  horse  power  is  the 
same  whether  the  fan  is  working  at  or  beyond  its 
capacity. 

In  considering  (79)  and  (80)  care  must  be 
taken  not  to  confuse  the  pressure  P,  corresponding 
to  the  tips1  of  the  floats,  with  the  pressure  in  the 
housing  at  the  outlet.  In  the  example  worked 
under  the  article  on  efficiency  it  was  found  that  a 
7-foot  fan  would  supply  the  required  quantity  of 
air  with  an  expenditure  of  8.3  horse  power,  while 
the  5^-foot  fan  required  an  expenditure  of  12.2 
horse  power  for  the  same  work.  This  is  not  in- 
consistent with  equations  (79)  and  (80),  because 
P  for  the  7-foot  fan  was  0.6  of  an  ounce,  while  for 
the  5^-foot  fan  it  was  0.91  of  an  .ounce.  Both  fans 
were  delivering  30000  cubic  feet  of  air  per  minute. 
Therefore  the  7-foot  fan  was  delivering  per  horse 
power 

30000 


8.3 


=  3610 


cubic  feet  of  air  per  minute;  while  the  5^-foot  fan 
was  delivering 


..  .460 


AIR    PER    HORSE    POWER.  141 

cubic  feet  of  air  per  minute  per  horse  power. 

From   (79)  we  get  that  the  air  delivered  per 
horse  power  per  minute  by  the  7-foot  fan  should  be 


3300 


P  (1  +  r2) 


=  3670 


0.6(1  + 0.7072) 

and  for  the  5^-foot  fan  we  get 
3300 


P(l+r2) 


2420 


0.91  (1  +  0.7072) 


There  is  a  slight  difference  in  the  results  ob- 
tained by  the  two  methods,  but  it  is  due  to  the 
fact  that  tables  were  used,  and  it  is  not  always 
possible  to  find  the  exact  value  desired  in  a  table 
and  we  are  obliged  to  take  the  nearest  value  given. 

Equation  (79)  has  been  used  to  calculate  the 
quantity  of  air  delivered  per  minute  per  horse 


142 


CENTRIFUGAL    FANS. 


power  by  fans  working  at  their  capacity  against 
different  pressures,  for  r  equal  0.5,  0.625  and  0.707; 
and  the  results  are  given  in  Table  XII. 


TABLE  XII. 

Air  per  minute  per  horse  power. 


r 

Pressure  in  ounces  per  square  inch. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

0.500 
0.625 
0.707 

26400 
23800 
22000 

13200 
11900 
11000 

8800 
7920 
7330 

6600 
5950 
5500 

5280 
4750 
4400 

4400 
3980 
3670 

3770 
3400 
3140 

3300 
2970 
2750 

2930 
2640 
2440 

2640 
2380 
2200 

CHAPTER  IX. 


Exhausters.  Heretofore  we  have  discussed 
fans  as  if  they  were  all  to  be  used  as  blowers,  we 
have  always  assumed  that  the  pressure  in  front 
of  the  inlet  was  that  of  the  atmosphere,  and  that 
the  pressure  in  the  housing  near  the  outlet  was 
greater  than  that  of  the  atmosphere.  When  a 
fan  is  used  as  an  exhauster,  its  action  so  far  as 
handling  air  is  concerned  is  in  no  way  different 
than  when  used  as  a  blower.  When  a  fan  used 
as  an  exhauster  is  attached  to  a  room  or  chamber 
and  the  inlet  opening  from  the  atmosphere  to  the 
chamber  is  closed,  there  is  a  vacuum  in  the  chamber 
and  a  pressure  equal  to  that  of  the  atmosphere  in 
the  housing.  The  vacuum  in  the  chamber  is  the 
same  number  of  ounces  below  the  pressure  of  the 
atmosphere  that  the  pressure  in  the  housing  would 
be  above  that  of  the  atmosphere  in  the  case  of  a 
blower  with  its  outlet  closed.  That  is  to  say,  the 
vacuum  is  expressed  by  the  same  number  of 

143 


144  CENTRIFUGAL    FANS, 

ounces  as  the  pressure  corresponding  to  the  velo- 
city of  the  tips  of  the  floats  of  the  fan  wheel.  When 
the  theoretical  area  of  the  opening  from  the  atmo- 
sphere into  the  chamber  is  equal  to  or  less  than 
the  blast  area,  the  pressure  in  the  chamber  is  less 
than  that  of  the  atmosphere  by  an  amount  equal  to 
the  pressure  corresponding  to  the  velocity  of  the 
tips  of  the  floats ;  and  when  the  theoretical  area  of 
the  opening  is  greater  than  the  blast  area  the 
pressure  in  the  chamber  is  less  than  that  of  the 
atmosphere  by  an  amount  that  is  less  than  the  pres- 
sure corresponding  to  the  velocity  of  the  tips  of 
the  floats. 

In  fan  work,  vacuums  are  expressed  in  ounces 
per  square  inch  just  as  pressures  are,  although 
the  word  vacuum  is  seldom  used.  It  is  quite 
common  to  speak  of  an  exhauster  "  working  at  a 
pressure  of  0.5  of  an  ounce,"  when  as  a  matter  of 
fact  it  is  not  working  against  any  pressure.  What 
is  meant  is  that  the  fan  is  being  run  at  such  a 
'speed  that  if  it  were  being  used  as  a  blower  there 
would  be  a  pressure  of  0.5  of  an  ounce  per  square 
inch  in  the  housing  if  the  theoretical  outlet  area 
were  equal  to  the  blast  area. 

An  exhauster  is  said  to  be  working  at  its  capa- 
city when  the  theoretical  inlet  area  from  the 
atmosphere  to  the  chamber  from  which  the  ex- 
hauster is  taking  air  is  equal  to  the  blast  area, 
and  when  the  outlet  of  the  fan  is  such  that  there 
is  a  perfectly  free  discharge  of  the  air  from  the 


EXHAUSTERS.  145 

fan  housing.  When  an  exhauster  is  working  at 
its  capacity  it  will  handle  exactly  the  same  quantity 
of  air  that  it  would  handle  if  working  at  its  capa- 
city as  a  blower.  That  is  to  say,  a  fan  us  d  as  an 
exhauster  and  working  at  its  capacity  against 
a  vacuum,  of  say,  0.6  of  an  ounce  will  handle 
exactly  the  same  quantity  of  air  that  it  would; 
handle  when  working  at  its  capacity  as  a  blower 
against  a  pressure  of  0.6  of  an  ounce.  This 
means,  of  course,  that  Tables  II.  and  HA  may  be 
used  for  exhausters  as  well  as  for  blowers.  In 
fact,  all  of  the  tables  given  here  apply  to  fans 
used  as  exhausters  as  well  as  to  fans  used  as 
blowers. 

When  a  fan  is  used  at  its  capacity  as  a  com- 
bination exhauster  and  blower  the  sum  of  the 
vacuum,  expressed  in  ounces  per  square  inch,  in 
the  chamber  from  which  the  air  is  being  drawn, 
and  the  pressure,  expressed  in  ounces  per  square 
inch,  in  the  housing  at  the  outlet  is  equal  to  the 
number  expressing  the  pressure  in  ounces  per 
square  inch  corresponding  to  the  velocity  of  the 
tips  of  the  floats.  Thus  if  a  fan  is  run  at  such  a 
speed  as  to  produce  a  pressure  of  0.7  of  an  ounce 
in  the  housing  when  working  at  its  capacity,  it 
can  be  made  to  work  at  the  same  speed  against  a 
vacuum  of  0.3  of  an  ounce  per  square  inch  and  a  pres- 
sure of  0.4  of  an  ounce  per  square  inch.  Or  to  put  it 
another  way,  we  may  say  that  if  a  fan  is  run  at 
such  a  speed  that  the  pressure  corresponding  to 


146  CENTRIFUGAL    FANS. 

the  velocity  of  the  tips  of  the  floats  is  0.7  of  an 
ounce  per  square  inch,  the  fan  will  work  at  its 
capacity  for  the  same  speed  against  any  combina- 
tion of  vacuum  and  pressure,  both  expressed  in 
ounces  per  square  inch,  whose  sum  is  0.7.  Thus 
there  may  be  a  vacuum  of  0.1  of  an  ounce  and  a 
pressure  of  0.6  of  an  ounce;  or  a  vacuum  of  0.5  of 
an  ounce  and  a  pressure  of  0.2  of  an  ounce.  And 
if  the  inlet  from  the  atmosphere  to  the  chamber 
in  which  the  vacuum  is  made,  and,  also,  the  outlet 
from  the  housing,  be  properly  adjusted,  the  fan 
will  deliver  for  each  combination  of  vacuum  and 
pressure  an  amount  of  air  equal  to  its  capacity. 


CHAPTER  X 


Housing.  In  order  to  get  good  results  from  a 
fan  used  as  a  blower  it  is  important  to  have  a 
proper  housing.  The  housing  should  fit  close  to 
the  sides  of  the  wheel,  and  be  so  made  as  to  allow 
equal  freedom  for  the  discharge  of  air  from  all 
parts  of  the  periphery.  The  air  in  the  housing 
tends  to  revolve  with  the  wheel  and  hence  the 
best  results  will  be  obtained  when  the  outlet 
opening  is  placed  so  that  the  air  glides  easily  and 
smoothly  into  it  without  any  abrupt  change  in 
the  direction  of  its  flow.  A  fan  wheel  placed  in  a 
rectangular  or  circular  casing  or  housing,  without 
a  scroll,  will  not  give  as  efficient  results  as  if  it 
were  placed  in  a  housing  having  a  proper  scroll  by 
which  the  air  is  gradually  led  to  the  outlet.  In 
the  case  of  a  circular  or  rectangular  housing  with 
the  outlet  opening  projecting  radially  from  the 
housing,  the  air  must  make  a  change  of  almost  a 
right  angle  in  its  direction  of  flow  in  order  to  enter 

147 


148  CENTRIFUGAL    FANS. 

the  outlet,  and  that  it  will  not  do,  especially  when 
the  wheel  is  working  at  comparatively  high  pres- 
sures. At  low  pressures  a  rectangular  or  circular 
housing  may  be  made  to  give  fairly  good  results, 
because  then  the  velocity  of  revolution  of  the  air 
in  the  housing  and  at  right  angles  to  the  outlet  is 
not  high.  The  higher  the  velocity  of  revolution 
of  the  air  in  the  housing  the  greater  is  the  diffi- 
culty of  making  the  air  change  its  direction  ab- 
ruptly, and  therefore,  the  greater  is  the  necessity 
of  having  a  housing  with  a  properly  constructed 
scroll  by  which  the  air  is  gradually  and  smoothly 
led  into  the  outlet  opening  without  any  abrupt 
change  in  either  velocity  or  direction.  The  wheel 
of  a  fan  should  always  revolve  in  the  direction  of 
the  increase  of  the  scroll,  from  the  point  where  it 
is  nearest  the  periphery  of  the  wheel  to  the  point 
where  it  is  farthest  from  the  periphery.  There  is 
probably  no  less  efficient  housing  or  one  which  re- 
duces the  air  delivery  capacity  of  a  wheel  more 
than  a  housing  with  a  proper  scroll  but  the  wheel 
revolving  backwards,  that  is  in  the  direction 
opposite  to  the  direction  of  the  increase  of  the 
scroll. 

The  dimensions  of  the  scroll  of  the  housing  of 
a  fan  wheel  depend  upon  the  diameter  of  the 
wheel  and  upon  the  diameter  of  the  inlet  opening. 
The  space  through  which  the  air  flows  towards 
the  outlet  between  the  periphery  of  the  wheel  and 
the  housing,  should  be  proportioned  between  the 


HOUSING.  149 

place  where  the  scroll  is  nearest  the  wheel  and  the 
place  where  the  scroll  is  farthest  from  the  wheel 
so  that  the  velocity  of  the  air  flowing  towards  the 
outlet  shall  be  the  same  at  every  point;  and  since 
the  discharge  from  the  periphery  of  the  wheel  into 
the  housing  is  to  be  uniform  at  all  points,  this 
means  that  the  scroll  of  the  housing  should  be  as 
nearly  as  possible  a  true  Archimedean  spiral. 

Let  Fig.  27  represent  the  housing  of  a  fan 
wheel  whose  diameter  is  D,  whose  width  is  W, 
and  whose  blast  area  is  A.  Let  the  diameter  of 
the  inlet  be  r  D  as  indicated  in  the  figure,  and  let 
the  fan  revolve  from  left  to  right  as  shown  by  the 
arrow.  At  the  point  a  where  the  outlet  begins, 
the  distance  of  the  scroll  from  the  periphery  of 
the  wheel  is  x\  at  6,  one-quarter  round  from  a,  the 

distance  is  — ;  at  c,  it  is  — ,    and   at   d,  it  is  -— :— 

4  2t  4. 

In  order  that  the  fan  may  work  at  its  capacity  the 
outlet  area  multiplied  by  its  coefficient  of  dis- 
charge must  not  be  less  than  the  blast  area  A.  If 
we  assume  that  the  coefficient  of  discharge  of  the 
outlet  is  1,  we  have,  since  the  area  of  the  outlet 
is  Wx, 

W  x  =  A 
From  which  we  get, 


*  ~~~~  W 


150  CENTRIFUGAL    FANS. 

From  (23)  we  have 

4  =  0.44  r3  D2 
And  this  value  of  A  in  the  expression  for  x  gives 

0.44  r3  D2 


(81) 


W 


FIG.  27. 


Since  the  distance  from  the  periphery  of  the 
wheel  to  the  housing   at  the   bottom  is  — ,     as 


HOUSING.  151 

shown  in  Fig.  27,  it  is  evident  that  the  height  of 

the  housing  cannot  be  less  than  D+  — .        And 

2i 

it  is  evident  that  for  a  wheel  of  a  given  diameter, 
the  height  of  the  housing  will  be  less  the  smaller 
we  make  oc.  But  from  (81)  it  is  evident  that  the 
greater  we  make  W,  the  width  of  the  wheel,  the 
smaller  will  be  the  value  of  oc.  Hence  the  wider 
we  make  the  wheel  the  lower  may  the  housing  be. 
It  is  usual  to  make  the  outlet  opening  square, 
and  to  make  the  actual  area  of  the  outlet  greater 
than  the  blast  area  in  order  to  allow  for  friction, 
and,  also,  because  the  coefficient  of  discharge  is 
not  always  1  as  was  assumed  in  deducing  (81). 
Therefore,  if  we  make  oc  equal  to  W  in  (81)  and 
make  the  actual  outlet  area  equal  to,  say,  1.5 
times  the  blast  area,  we  get 

W2  =  1.5  X  0.44  r*D2 

=  0.66  r*  D2 
From  which  we  get 
(82)  W  =  x/0.66  r3  D2 

If  now  we  make  r  equal  0.707  in  (82)  we  gel 
W  =  v/0.66x  0.7073£>2 
-  0.48  D 


152  CENTRIFUGAL    FANS. 

This  shows  the  reason  for  the  custom,  which 
prevails  with  many  manufacturers,  of  making  the 
width  of  a  fan  equal  to  one-half  of  the  diameter 
of  the  wheel  when  the  diameter  of  the  inlet  opening 
is  equal  to  0.707  of  the  diameter  of  the  wheel. 

If  r  were  0.625  we  should  have 

W  =  V0.66X  0.6253£>2 
=  0.40  D 

Some  manufacturers  make  what  is  called  a 
"  narrow  "  fan,  whose  width  is  about  three- 
eighths  of  the  diameter  of  the  wheel ;  although  most 
fans  used  for  heating  and  ventilating  work  are 
made  with  a  width  equal  to  one-half  the  diameter 
of  the  wheel,  irrespective  of  the  ratio  of  the  diam- 
eter of  the  inlet  opening  to  the  diameter  of  the  wheel. 
When  the  outlet  is  made  square  and  the  width  of 
the  fan  is  one-half  the  diameter  of  the  wheel  the 
actual  area  of  the  outlet  opening  is  about  1.6  the 
blast  area,  when  r  is  0.707. 

Instead  of  making  the  bottom  of  the  outlet 
at  a  in  Fig.  27,  it  is  usually  made  at  a  point  a' 
about  one-eighth  of  the  circumference  round  from 
a.  The  outlet  is  then  as  indicated  by  the  dotted 
lines,  and  the  air  which  escapes  from  the  periphery 
of  the  wheel  between  a  and  a'  passes  directly  into 
the  outlet  without  passing  into  the  scroll  at  all. 
Hence  instead  of  all  of  the  air  .discharged  by  the 


HOUSING.  153 

fan  being  obliged  to  pass  through  the  space  be- 
tween the  point  a  and  the  scroll  only  f  of  it  must 
pass  through  this  space.  And  in  order  that  the 
velocity  of  the  air  which  passes  through  this  space 
shall  be  the  same  as  the  velocity  of  the  air  passing 
through  the  outlet,  the  area  of  the  space  should 
be  I  of  the  area  of  the  outlet.  Since  the  area  of 
this  space  is  %  W  and  the  area  of  the  outlet  is  W2, 
we  have 

7W2 

%W  =   ~*~ 

o 

and 

7  W 
(83)  x  =  ~ 

If  now  we  make  W  equal  to  one-half  the  dia- 
meter of  the  wheel  we  get 


(84)  oc  =  ~  ==  0.44  £>,  about. 


From  Fig.  27  we  see  that  at  b  the  distance  of 

oc 
the  scroll  from  the  wheel  is—  equal   0.11  D\    at 

c  it  is  — ,   equal  0.22  D\  and  at  d  it  is   —  ,     equal 
2i  4 

to  0.33  D. 

% 
The  height  of  the  housing  is  equal  to  x  +  D  -f  — 


154  CENTRIFUGAL    FANS. 

equal   1.66Z);  and  the   length   of  the  housing  is 

3  x 

equal  to    — -  x  +  D  -f  — ,  equal  1.44  D. 

The  value  of  x  given  above  is  for  a  width  of  fan 
equal  to  one-half  the  diameter  of  the  wheel,  and 
we  have  shown  that  this  is  the  width  proper  for 
a  fan  whose  inlet  opening  is  0.707  the  diameter 
of  the  wheel.  We  have  shown  that  for  a  fan  with 
a  square  outlet,  and  an  inlet  equal  to  0.625  the 
diameter  of  the  wheel,  the  width  of  the  fan  should 
be  about  0.4  the  diameter  of  the  wheel,  although 
it  is  often  made  f  the  diameter  of  the  wheel. 
When  the  width  of  the  fan  is  f  the  diameter  of  the 
wheel  x  becomes 


7  W         7x3£> 
8  8x8 

21  D 


64 


0.328  D 


Fans  are  sometimes  made  with  a  width  equal 
to  half  the  diameter  of  the  wheel,  an  inlet  equal 
to  0.625  the  diameter  of  the  wheel,  and  a  square 
outlet.  These  fans  are  usually  made  with  hous- 
ings so  proportioned  that  x  is  equal  to  about 
0.30  D.  The  height  of  housings  of  such  fans  is 
equal  to  1.45D.  In  general,  we  may  say  that 
for  fans  whose  width  is  equal  to  one-half  the  diam- 


HOUSING. 


155 


eter  of  the  wheel,  x  is  0.44  D  when  the  inlet  is 
0.707  the  diameter  of  the  wheel;  and  x  is  0.30  D 
when  the  inlet  is  0.625  the  diameter  of  the  wheel. 
Having  decided  upon  the  value  of  x  the  next 
thing  is  to  draw  the  scroll.  The  scroll  is  usually 


FIG.  28. 


a  three  arc  scroll,  that  is  to  say  it  is  made  up  of 
arcs  of  three  different  radii.  Referring  now  to 
Fig.  28  it  is  seen  that  the  distance  of  the  point  b 

D       x 

from  the  center  c  of  the  wheel  is  —  -f  —  ;     the 

2         4 


156  CENTRIFUGAL    FANS. 


D  X 

distance  of  c    from    o    is  —    H-    — ,  and  the  dis- 

2*  £ 

tance  of  d  from  o  is    —   -f    '— .      The    distance 

3  x  x 

from   b   to   d  is         '+/>+—,   which   is  ius't 
4  4 

twice  the  distance  of  c  below  the  point  o.     Hence 
we  may  make  the  part  b  c  d  of  the  scroll  a  semi- 

D          x 
circle  whose  radius    is   —    4-    -^-.     The  center  of 

this  circle  will  be  at  o' ,  to  the  left  of  o  a  distance 

D       x 
o'  o,  which    is   equal    to  —  +  —  minus    the  dis- 

— '          2i 

D       x 
tance  o  b.     But  o  b  is  —  H-  — ,    and   hence  o'o  is 

—  4 

X 

T* 

The  part  d  a  of  the  scroll  must  be  the  arc  of  a 
circle  whose  center  is  on  the  line  o  b  and  whose 
radius  is  equal  to  the  distance  of  the  point  a,  the 
top  of  the  outlet,  above  the  center  of  the  wheel, 

which  is  —  +  x.     The  center  of  this  arc  will  be  at 

o" ',  to  the  right  of  o  a  distance  o  o"  equal  to  —  -f  x 

u 

D      3x 

minus  the  distance  o  d.     But  o  d  is  -;-  +  — ,  and 

2i          4 

hence  o  o"  is  — . 

The  part  e  b  of  the  scroll  may  be  drawn  about 


HOUSING.  157 

o"  as  a  center  with  a  radius  equal  to  the  distance 

D 


o 


D       x        x  .   D 

b  minus  o  o" ,  which  is  —  -h  —  -    — ,  equal  — . 


Hence  if  we  call  R^  the  radius  of  the  arc  e  b\ 
R2  that  of  the  arc  bed]  and  R3  that  of  the  arc 
from  d  to  the  top  of  the  fan,  we  have 


*.-! 


D 


The  height,  T,  of  the  scroll  is  equal  to 
and  the  height  of  the  fan  from  the  foundation  to 
the  top  of  the  scroll  is  usually  one  or  two  inches 
greater  than  the  height  of  the  scroll. 

For  a  fan  whose  width  is  one-half  the  diam- 
eter of  the  wheel  and  whose  inlet  is  0.707  the  diam- 
eter of  the  wheel  x  is  equal  to  0.44  D,  and  hence 
we  have  the  distance  o'o,  equal  distance  o  o",  is 

oc 
equal  -j-'or  0.11  D,  and 


158  CENTRIFUGAL    FANS. 

/?!•  =   0.5  D 

R2  =  0.72  D 
R3  =  0.94  D 
T  =  1.66  D 

For  a  fan  whose  width  is  about  one-half  the 
diameter  of  the  wheel  and  whose  inlet  is  0.625 
the  diameter  of  the  wheel  we  have  said  that  %  is 
about  0.30  D,  and  hence  we  have  the  distance  o'  o, 

JC 

equal  distance  o  on ',  is  equal—  or  0.075  D,  and 

Rl  -  0.5  D 
R2  =  0.65  D 
Ra  =  0.80  D 
T  -  1.45  D 

The  side  pieces  and  the  scroll  piece  of  the 
housing  of  a  fan  when  made  of  sheet  steel  must 
be  braced  with  angle  irons  and  made  sufficiently 
thick  to  resist  the  pressure  of  the  air  and  the 
straining  action  due  to  the  movement  of  the 
wheel.  The  heavier  the  braces  and  the  more 
there  are,  the  thinner  may  be  the  plates  of  the 
side  pieces  and  the  scroll  piece.  There  seems  to 


DIMENSIONS    OF    HOUSINGS.  159 

be  no  particular  rule  or  formula  followed  in  deter- 
mining the  thickness  of  the  plates  used  or  -  the 
size  of  the  angle  irons  used  for  bracing  them,  and 
yet  there  seems  to  be  a  rather  remarkable  agree- 
ment in  the  practice  of  the  different  manufac- 
turers. 


Dimensions  of  Housings.  In  laying  out  fan 
work  it  is  often  necessary  to  know  approximately 
at  least  the  space  that  will  be  occupied  by  a  fan 
having  a  wheel  of  a  certain  diameter  with  a  given 
ratio  of  inlet  to  diameter  of  wheel.  And  in  order 
to  facilitate  the  work  of  the  designer  in  such  cases 
the  following  tables,  showing  the  various  dimen- 
sions of  the  housings  of  fans  are  given.  The 
dimensions  given  in  the  tables  have  been  calcu- 
lated not  taken  from  the  catalogue  of  any  manu- 
facturer, and  hence  it  is  not  likely  that  they  will 
be  found  to  agree  exactly  with  the  dimensions  of 
any  manufacturer.  They  are  only  approximate, 
and  are  intended  only  to  enable  a  designer  to 
obtain  a  fairly  accurate  estimate  of  the  space  that 
a  fan  will  occupy.  The  exact  dimensions  of  the 
housing  of  a  fan  of  a  certain  make  will  depend 
upon  the  details  of  construction  adopted  by  the 
maker  and  must  be  obtained  from  him  if  they  are 
desired.  The  dimensions  are  given  in  inches  in 
all  cases. 

Tables  XIII.,  XIV.  and  XV.  are  for  fans  for 


160  CENTRIFUGAL    FANS. 

which  the  ratio,  r,  of  diameter  of  inlet  to  diameter 
of  wheel  is  0.707;  and  Tables  XVI.  ,  XVII.  and 
XVIII.  are  for  fans  for  which  r  is  0.625. 

The  dimensions  in  Table  XIII.  have  been  calcu- 
lated by  the  following  equations,  in  which  D  is 
the  diameter  of  the  wheel  in  feet. 

/  =  8.48  D  O  =  6  D 

G  =  17.3  D  T  =  19.9  D+l 

J  =  9.96  D  L  =  7.32  D 
Q  =  8.64  £>+! 

In  Table  XIV.  all  dimensions  except  T  and  Q 
are  the  same  as  in  Table  XIII.,  and 


T  =  15.5 

Q  =  4.2  D  +  z 

z  is  two  inches  for  wheels  4  feet  or  less  in  diam- 
eter; 2^  inches  for  wheels  larger  than  4  feet  up  to 
6  feet  ;  3  inches  for  wheels  larger  than  6  feet  up  to 
9  feet;  and  4  inches  for  wheels  larger  than  9  feet. 

In  Table  XV.  all  the  dimensions  except  T  and  Q 
are  the  same  as  in  Table  XIV.,  and  here 

T  =  12.84£>  +  Z 
Q  =    4.2D  +  Z 

z  has  the  same  value  as  in  Table  XIV. 


DIMENSIONS    OF    HOUSINGS. 


161 


TABLE  XIII. 
Full  housed,  top,  horizontal  discharge  fan,  r=0.707. 


Diameter 
of  wheel 


Dimensions  of  housings  in  inches. 


in  feet. 

/ 

O 

G 

T 

/ 

L 

Q 

3 

25 

18 

52 

61 

30 

22 

27 

a* 

30 

21 

61 

71 

36 

25 

31 

4 

34 

24 

69 

81 

40 

29 

36 

4* 

38 

27 

78 

91 

45 

33 

40 

5 

42 

30 

87 

101 

50 

37 

44 

5* 

47 

33 

95 

110 

55 

40 

49 

6 

51 

36 

104 

120 

60 

44 

53 

6* 

55 

39 

113 

130 

65 

48 

57 

7 

59 

42 

121 

140 

70 

51 

61 

8 

68 

48 

139 

160 

80 

59 

70 

9 

76 

54 

156 

180 

90 

66 

79 

10 

85 

60 

173 

200 

100 

73 

87 

11 

93 

66 

191 

220 

110 

81 

96 

12 

102 

72 

208 

240 

120 

88 

105 

162 


CENTRIFUGAL    FANS. 


T 


(-0 1 


TABLE  XIV. 
Three  quarter  housed,  top,  horizontal  discharge  fan,  r  —  0.707. 


Diameter 
of  wheel 
in  feet. 

Dimensions  of  housings  in  inches. 

/ 

0 

G 

T 

J 

L 

Q 

3 

25 

18 

52 

48 

30 

22 

15 

3* 

30 

21 

61 

56 

36 

25 

17 

4 

34 

24 

69 

64 

40 

29 

19 

'  4j 

38 

27 

78 

71 

45 

33 

21 

5 

42 

30 

87 

80 

50 

37 

24 

•H 

47 

33 

95 

88 

55 

40 

26 

6 

51 

36 

104 

96 

60 

44 

28 

6* 

55 

39 

113 

104 

65 

48 

30 

;  7 

59 

42 

121 

112 

70 

51 

32 

8 

68 

48 

138 

127 

80 

58 

37 

9 

76 

54 

156 

143 

90 

66 

41 

10 

85 

60 

173 

159 

100 

73 

46 

11 

93 

66 

190 

175 

110 

80 

50 

12 

102 

72 

208 

190 

120 

88 

54 

DIMENSIONS    OF    HOUSINGS. 


163 


I - 


TABLE  XV. 
Three  quarter  housed,  bottom,  horizontal  discharge  fan,  r  =  0.707. 


Diameter 

Dimensions  of  housings  in  inches. 

in  feet. 

/ 

O 

G 

T 

J 

L 

Q 

3 

25 

18 

52 

41 

30 

22 

15 

3* 

30 

21 

61 

47 

36 

25 

17 

4 

34 

24 

69 

53 

40 

29 

19 

H 

38 

27 

78 

60 

45 

33 

21 

5 

42 

30 

87 

67 

50 

37 

24 

5i 

47 

33 

95 

73 

55 

40 

26 

6 

51 

36 

104 

80 

60 

44 

28 

61 

55 

39 

113 

87 

65 

48 

30 

7 

59 

42 

121 

93 

70 

51 

33 

gS  8 

68 

48 

138 

106 

80 

58 

37 

9 

76 

54 

156 

119 

90 

66 

41 

10 

85 

60 

173 

132 

100 

73 

46 

11 

93 

66 

190 

146 

110 

80 

50 

12 

102 

72 

208 

158 

120 

88 

55 

164 


CENTRIFUGAL    FANS. 


[->• — i 


_i 


TABLE  XVI. 
Full  housed  top,  horizontal  discharge  fan,  r  =  0.625. 


Diameter 
of  wheel 
in  feet. 

Dimensions  of  housings  in  inches. 

I 

0 

G 

T 

J 

L 

Q 

3 

23 

18 

47 

53 

26 

21 

24 

3* 

26 

21 

55 

62 

31 

24 

28 

4 

30 

24 

63 

71 

35 

28 

32 

4* 

34 

27 

70 

79 

39 

31 

36 

5 

38 

30 

78 

88 

43 

35 

40 

5* 

41 

33 

86 

97 

48 

38 

44 

6 

45 

36 

94 

105 

52 

42 

48 

*| 

49 

39 

101 

114 

56 

45 

52 

7 

53 

42 

109 

123 

61 

48 

56 

8 

60 

48 

125 

140 

70 

55 

63 

9 

68 

54 

140 

158 

78 

62 

71 

10 

75 

60 

156 

175 

87 

69 

79 

11 

83 

66 

172 

193 

96 

76 

87 

12 

90 

72 

187 

210 

104 

83 

95 

DIMENSIONS    OF    HOUSINGS. 


165 


o j 


TABLE  XVII. 
Three  quarter  housed,  top,  horizontal  discharge  fan,  r=«0.625. 


Diameter 
of  wheel 
in  feet. 

Dimensions  of  housings  in  inches. 

/ 

0 

G 

T 

J 

L 

Q 

3 

23 

18 

47 

42 

26 

21 

13 

3* 

26 

21 

55 

49 

31 

24 

15 

4 

30 

24 

63 

55 

35 

28 

17 

4* 

34 

27 

70 

63 

39 

31 

19 

5 

38 

30 

78 

69 

43 

35 

21 

5* 

41 

33 

86 

76 

48 

38 

23 

6 

45 

36 

93 

83 

52 

41 

25 

6* 

49 

39 

101 

90 

56 

45 

27 

7 

53 

42 

109 

96 

61 

48 

29 

8 

60 

48 

125 

110 

70 

55 

33 

9 

68 

54 

140 

123 

78 

62 

38 

10 

75 

60 

156 

138 

87 

69 

41 

11 

83 

66 

172 

151 

96 

76 

45 

12 

90 

72 

187 

164 

104 

83 

49 

166 


CENTRIFUGAL    FANS. 


TABLE  XVIII. 
Three  quarter  housed,  bottom,  horizontal  discharge  fan,  r =0.625. 


Diameter 
of  wheel 
in  feet. 

Dimensions  of  housings  in  inches. 

/ 

0 

G 

T 

1 

L 

Q 

3 

23 

18 

47 

38 

26 

21, 

13 

3* 

26 

21 

55 

43 

31 

24 

15 

4 

30 

24 

63 

48 

35 

28 

17 

4* 

34 

27 

70 

54 

39 

31 

19 

5 

38 

30 

78 

60 

43 

35 

21 

5* 

41 

33 

86 

66 

48 

38 

23 

6 

45 

36 

93 

72 

52 

41 

25 

6* 

49 

39 

101 

78 

56 

45 

27 

7 

53 

42 

109 

84 

61 

48 

29 

8 

60 

48 

125 

97 

70 

55 

33 

9 

68 

54 

140 

107 

78 

62 

37 

10 

75 

60 

156 

120 

87 

69 

41 

11 

83 

66 

172 

131 

96 

76 

45 

12 

"  90 

72 

187 

143 

104 

83 

49 

DIMENSIONS    OF    HOUSINGS.  167 

The  dimensions  in  Table  XVI.  have  been  cal- 
culated by  the  following  equations: 

7  =  7.5  D  O  =  6£> 

G  =  15.6  D  T  =  17.4  D+l 

J  =  8.7  D  L  =  6.9  D 
Q  =  7.8  D+l 

In  Tables  XVII.  and  XVIII.  all  the  dimen- 
sions except  T  and  Q  are  the  same  as  in  Table  XVI. 
The  equations  for  T  and  Q  in  Table  XVII.  are 

r  =  13.35  D  +  z 
Q  =  3.75  D  +  z 

The  equations  for  T  and  Q  in  Table  XVIII.  are 
T  =  11.55 
Q  =  3.75 

The  values  of  z  used  in  Tables  XVII.  andXVIII. 
are  the  same  as  those  given  in  the  explanation  of 
Table  XIV. 


168  CENTRIFUGAL    FANS. 

Shaft.  When  the  power  necessary  to  drive  a 
fan  is  known  it  is  an  easy  matter  to  calculate  the 
size  of  shaft  required  for  it,  but  a  manufacturer 
designing  a  line  of  fans  is  never  sure  exactly  what 
will  be  the  worst  conditions  under  which  a  fan 
will  run  and  as  it  will  not  pay  to  design  a  fan  for 
every  condition  he  designs  all  of  the  ordinary 
commercial  fans  for  what  is  probably  the  worst 
conditions  of  ordinary  use.  And  as  the  ideas  of 
different  manufacturers  are  not  the  same  as  to 
what  are  probably  the  worst  conditions  under 
which  an  ordinary  fan  will  be  used,  it  results  that 
the  fans  of  different  manufacturers  differ  more  in 
such  details  as  the  size  of  shaft,  the  kind  of  bear- 
ings, diameters  of  bolts,  etc.,  than  in  other  things. 

The  shafts  of  small  fans  are  usually  made 
larger  in  proportion  to  the  diameter  of  the  wheels 
than  are  shafts  of  large  fans.  This  is  so  because 
it  is  not  advisable  to  have  a  shaft  less  than  an 
inch  and  a  half  on  even  a  small  fan  having  a  wheel 
3  feet  in  diameter,  even  although  such  a  shaft  may 
be  larger  than  is  actually  necessary  for  the  work 
the  fan  will  be  called  upon  to  do ;  and,  also,  because 
large  fans  are  seldom  worked  at  as  high  a  pressure 
as  the  smaller  ones. 

A  safe  practice  for  fans  having  wheels  not 
smaller  than  3  feet  in  diameter  and  not  larger  than 
7  feet,  is  to  make  the  diameter  of  the  shaft  in  inches 
equal  to  one  half  the  diameter  of  the  wheel  in  feet. 

This  rule  if  applied  to  large  fans  will  give  a 


SHAFT.  169 

shaft  which  is  unnecessarily  large,  so  for  fans 
with  wheels  not  less  than  7  feet  nor  more  than  12 
feet  in  diameter  we  may  make  the  diameter  of  the 
shafts  equal  to  If  inches  plus  one  quarter  of  the 
diameter  of  the  wheel  in  feet. 

Thus,  we  should  use  for  ordinary  heating  work 
a  2-inch  shaft  with  a  4-foot  wheel,  and  a  4J-inch, 

equal  —  +  If,  shaft  for  a  10-foot  wheel. 


CHAPTER  XL 


Cone  Wheels.  The  name  "  cone  wheel "  is 
applied  to  a  form  of  single  inlet  centrifugal  fan 
wheel  that  is  used  either  without  a  housing  or 
with  a  housing  that  does  not  fit  close  to  the  wheel, 
has  no  scroll  and  is  large  as  compared  to  the  wheel. 
The  proportions  of  the  cone  wheels  are  entirely 
different  from  those  of  other  centrifugal  fans,  but 
the  general  formulas  which  have  been  deduced  for 
centrifugal  fans  apply  to  the  cone  wheels  as  well 
as  to  the  other  forms  of  centrifugal  fans.  These 
fans,  however,  do  not  give  good  results  when  the 
pressure  against  which  they  have  to  work  is  at  all 
high.  They  stand  intermediate  between  the  ordi- 
nary disc  fan  which  will  work  against  very  low 
pressures  only,  probably  not  over  \  or  f  of  an 
ounce,  and  the  regular  centrifugal  blower  with 
close  fitting  housing  having  a  proper  scroll,  which 
will  work  against  a  pressure  of  several  ounces  per 
square  inch.  It  is,  of  course,  impossible  to  say 

170 


:  CONE    WHEELS.   -'  171 

what  is  the  limit  of  pressure  against  which  a  cone 
wheel  will  work.  Tests  have  been  made  which 
show  that  they  will  work  against  a  pressure  of  an 
ounce  or  an  ounce  and  a  half.  Even  for  low 
pressures  they  are  not  as  economical  to  operate 
as  the  ordinary  centrifugal  fan,  and,  in  the  opinion 
of  the  writer,  they  are  not  to  be  used  for  heating 
or  ventilating  work  when  it  is  possible  to  use  an 
ordinary  centrifugal  with  a  close  fitting  housing 
and  a  proper  scroll.  Where  they  are  used,  care 
should  be  taken  to  see  that  they  are  properly 
erected  with  a  free  inlet  and  a  housing  so  arranged 
and  porportioned  that  there  can  be  a  free  dis- 
charge of  the  air  from  all  points  of  the  periphery. 
A  free  entrance  for  the  air  at  the  inlet  and  a  free 
discharge  at  the  periphery  are  as  absolutely  neces- 
sary for  fans  of  this  type  as  for  those  of  the  ordi- 
nary centrifugal  type;  and  a  lack  of  these  essential 
features  has  been  the  cause  of  failure  to  give  satis- 
factory results. 

Fig.  29  shows  a  section  parallel  to  the  axis  of 
a  cone  wheel  in  place  ready  for  operation;  and 
Fig.  30  shows  a  view  looking  at  the  inlet.  The 
housing  in  this  case  consists  of  a  rectangular  room 
4  in  which  are  the  wheel,  one  bearing  of  the  shaft 
B,  and  the  driving  pulley  C.  The  air  enters 
through  the  inlet  E  and  passes  along  the  cone  F 
to  the  floats  G  which  are  fastened  to  the  side 
plates  H.  The  air  passes  between  the  side  plates 
H  into  the  housing,  and  from  there  passes  out 


172 


CENTRIFUGAL    FANS. 


FlG,   29. 


CONE    WHEELS 


173 


FIG.  30. 


174  CENTRIFUGAL    FANS. 

through  proper  openings.  The  distance  between 
the  periphery  of  the  fan  wheel  and  the  ceiling, 
side  walls,  or  floor  of  the  housing  should  be  ample 
for  the  free  discharge  of  the  air  at  every  point, 
and  it  will  be  found  well  to  make  this  distance  equal 
to  at  least  one-quarter  the  diameter  of  the  wheel. 
In  Fig.  29  it  will  be  noticed  that  one  of  the  shaft 
bearings  is  shown  in  front  of  the  inlet.  This  con- 
struction should  be  avoided  whenever  possible 
and  both  bearings  put  back  of  the  wheel,  making 
the  wheel  "  overhung,"  and  giving  a  perfectly 
free  inlet.  It  must  be  remembered  that  any  im- 
pediment or  obstruction  to  the  flow  of  the  air 
into  the  inlet,  such  $s  must  be  offered  by  a  bearing' 
or  a  pulley  close  to  the  inlet,  prevents  the  air  from 
entering  the  wheel  and  thereby  reduces  the  capa- 
city of  the  fan. 

Cone  wheels  are  almost  uniformly  made  with 
a  width  equal  to  one-quarter  the  diameter  of  the 
wheel,  and  an  inlet  opening  whose  diameter  is 
three-fourths  the  diameter  of  the  wheel.  The 
width  of  the  periphery  is  usually  three-fourths  the 
width  of  the  fan.  The  floats  are  usually  curved, 
and  the  wheel  is  supposed  to  be  revolved  so  that 
the  convex  side  of  the  floats  move  forward,  as 
shown  by  the  arrow  in  Fig.  30.  It  is  probable 
that  this  form  of  float  is  not  so  good  as  a  properly 
designed  float  with  its  concave  side  forward,  but 
it  is  the  form  generally  used. 

Since  the  diameter  of  the  inlet  is  three  fourths 


CONE    WHEELS.  175 

the  diameter  of  the  wheel  r  in  (18)  is  0.75.     Hence 
the  expression  for  the  capacity  of  a  cone  wheel  is 

(85)  C  =  2280  i*  D2 

-  962  D2 


For  all  practical  purposes  it  is  near  enough  to 
the  truth  to  say  that 

(86)  C  =  950  D2  Vp" 

Table  XIX.  giving  the  capacities  of  cone 
wheels  of  various  diameters  working  against  dif- 
ferent pressures  per  square  inch,  has  been  calcu- 
lated by  (80). 

When  a  cone  wheel  is  working  at  or  less  than 
its  capacity  the  number  of  revolutions  which  it 
must  make  in  order  to  give  a  certain  pressure  in 
ounces  per  square  inch  may  be  determined  by 
(47)  or  by  means  of  Table  VI. 

The  horse  power  required  to  run  a  cone  wheel 
when  working  at  its  capacity  is  obtained  by 
making  r  in  (60)  equal  to  0.75.  Doing  this  we  get 


(87)  H      CP 


2100 


Table  XX.   gives  the   horse  power  as   calcu- 


176 


CENTRIFUGAL    FANS. 


TABLE  XIX. 
Capacities  of  cone  wheel  fans. 


Diameter 
of  wheel 
in  feet. 

Pressure  in  ounces  per  square  inch. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

3 

2700 

3800 

4700 

5400 

6100 

6600 

7200 

7600 

3* 

3700 

5200 

6400 

7400 

8200 

9000 

9700 

10400 

4 

4800 

6800 

8300 

9600 

10700 

11800 

12700 

13600 

4* 

6100 

8600 

10500 

12200 

13600 

14900 

16100 

17200 

5 

7500 

10600 

13000 

15000 

16800 

18400 

19800 

21200 

5* 

9100 

12800 

15700 

18200 

20300 

22300 

24100 

25700 

6 

10800 

15300 

18700 

21600 

24200 

26500 

28600 

30600 

9* 

12700 

17900 

22000 

25400 

28400 

31100 

33600 

35900 

7 

14700 

20800 

25500 

29500 

33000 

36100 

39000 

41600 

8 

19200 

27200 

33300 

38500 

43000 

47100 

50800 

54400 

9 

24300 

34400 

42100 

48600 

54400 

59600 

64400 

68800 

10 

30000 

42500 

52000 

60000 

67200 

73500 

79500 

84800 

11 

36300 

51400 

63000 

72600 

81300 

89000 

96000 

103000 

12 

43300 

61200 

75000 

86500 

96800 

106000 

114000 

122000 

TABLE  XX. 

Horse  power  required  for  cone'wheels. 


Diameter 
of  wheel 
in  feet. 

Pressure  in  ounces  per  square  inch. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

3 

0.13 

0.36 

0.67 

1.03 

1.45 

1.89 

2.40 

2.90 

aj 

0.18 

0.50 

0.91 

1.41 

1.95 

2.57 

3,24 

3.96 

4 

0.23 

0.65 

1.19 

1.83 

2.55 

3.37 

4.23 

5.18 

4* 

0.29 

0.82 

1.50 

2.32 

3.24 

4.26 

5.36 

6.55 

5 

0.36 

1.01 

1.86 

2.86 

4.00 

5.26 

6.60 

8.08 

5* 

0.43 

1.22 

2.24 

3.47 

4.83 

6.37 

8.03 

9.80 

6 

0.51 

1.46 

2.67 

4.12 

5.76 

7.57 

9.53 

11.7 

6* 

0.63 

1.70 

3.14 

4.84 

6.75 

8.90 

11.2 

13.7 

7 

0.70 

1.98 

3.64 

5.62 

7.86 

10.3 

13.0 

15.9 

8 

0.91 

2.59 

4.75 

7.33 

10.2 

13.5 

17.0 

20.7 

9 

1.16 

3.28 

6.02 

9.26 

13.0 

17.0 

21.5 

26.2 

10 

1.43 

4.05 

7.43 

11.4 

16.0 

21.0 

26.5 

32.3 

11 

1.73 

4.90 

9.00 

13.9 

19.4 

25.4 

32.0 

39.2 

12 

2.07 

5.83 

10.7 

16.5 

23.0 

30.3 

38.0 

46.5 

CONE    WHEELS.  177 

lated  by  (87)  required  to  run  cone  wheels  of  dif- 
ferent diameters  when  working  at  their  capacities 
against  various  pressures. 

i  The  size  of  engine  of  motor  required  for  a  cone 
wheel  is  determined  by  dividing  the  horse  power 
required  to  run  the  wheel,  as  found  from  Table  XX, 
by  the  efficiency  of  the  engine  or  motor.  The 
efficiency  of  the  ordinary  small  engine  may  be 
taken  as  f,  and  that  of  the  ordinary  motor  either 
direct  or  alternating  current  may  be  taken  as  f . 

Tables  VI,  XIX  and  XX  enable  us  to  deter- 
mine all  that  it  is  necessary  to  know  in  order  to 
select  a  cone  wheel  for  a  given  work.  Table  XIX 
unables  us  to  determine  the  diameter  of  the  wheel 
required;  Table  VI  enables  us  to  determine  the 
number  of  revolutions  at  which  it  must  be  run; 
and  Table  XX  enables  us  to  determine  the  horse 
power  required  to  run  it. 

EXAMPLE: — Determine  the  size  of  a  cone  wheel 
required  to  deliver  30,000  cubic  feet  of  air  per 
minute  against  a  pressure  of  0.3  of  an  ounce  per 
square  inch.  Also  determine  the  number  of  revolu- 
tions at  which  the  wheel  must  be  run,  and  the  horse 
power  required  to  run  it. 

Looking  in  Table  XIX  under  the  column  headed 
0.3,  we  find  that  the  nearest  number  to  30000  is 
33300,  which  is  opposite  an  8-foot  wheel.  Hence 
we  will  use  an  8-foot  wheel. 

Now  looking  in  Table  VI  under  the  column 
headed  0.3  and  opposite  the  8-foot  wheel  we  find 


178  CENTRIFUGAL    FANS. 

113.  Hence  the  8-foot  wheel  must  be  run  at  113 
revolutions  per  minute. 

From  Table  XX  we  find  that  the  horse  power 
required  to  run  an  8-foot  cone  wheel  when  working 
at  its  capacity  against  a  pressure  of  0.3  of  an  ounce 
per  square  inch  is  4.75. 

The  horse  power  of  the  engine  required  to  run 
the  fan  will  be 


4.75 


The  diameter  of  the  cylinder  and  the  length  of 
stroke  of  the  engine  will  depend  upon  the  pressure 
of  steam  carried  and  the  number  of  revolutions  the 
engine  is  to  make  per  minute.  If  the  engine  is  to 
be  of  the  direct  connected  type,  so  that  the  fan 
wheel  will  be  mounted  directly  on  the  shaft  of  the 
engine,  it  must  make  the  same  number  of  revolu- 
tions that  the  fan  does. 

The  size  of  motor  required  to  run  the  fan  will  be 


4  75 

'        =*  6.35  horse  power. 
u.7o 


It  is  interesting  to  compare  the  cone  fan  re- 
quired by  the  conditions  of  the  problem  with  anj 
ordinary  centrifugal  fan  of  the  blower  type,  of  thei 


CONE    WHEELS.  179 

size  required  for  the  work  and  having  an  inlet  whose 
diameter  is  0.625  the  diameter  of  the  fan  wheel. 

Table  HA  shows  that  for  a  fan  in  which  r  is 
0.625,  a  10-foot  wheel  will  be  required  to  deliver 
30000  cubic  feet  of  air  per  minute  against  a  pres- 
sure of  0.3  of  an  ounce  per  square  inch.  Table 
VI.  shows  that  this  wheel  must  make  90  revolu- 
tions per  minute.  And  Table  VIIlA  shows  that 
3.82  horse  power  will  be  required  to  run  the  wheel. 

The  difference  between  the  power  stated  as  re- 
quired for  the  cone  wheel  and  the  blower  wheel  is 
greater  than  it  should  be  because  the  cone  wheel 
chosen  was  capable  of  delivering  10  per  cent, 
more  air  per  minute  than  was  actually  required. 
The  horse  power  actually  required  by  the  cone 
wheel  when  delivering  30000  cubic  feet  instead  of 

33300  is  about  ^j-p  =  4.32.      This,    however,   is 

still  greater  than  the  power  required  for  the 
blower  fan  by  about  13  per  cent.  In  other 
words  the  cone  wheel  would  be  of  smaller 
diameter  than  the  blower  wheel,  and  would  there- 
fore probably  cost  a  little  less ;  but  the  cone  wheel 
would  cost  13  per  cent,  more  to  operate. 


CHAPTER  XII. 


Disk  Fans.  While  this  book  is  intended  as  a 
treatise  on  centrifugal  fans  it  would  not  be  com- 
plete without  some  reference  to  disk  fans  which 
operate  in  a  totally  different  way  from  centrifugal 
fans.  The  centrifugal  fan  as  we  have  shown 
operates  upon  the  principal  of  a  vortex,  but  the 
disk  fan  operates  like  a  screw.  The  disk  fan 
consists  essentially  of  disks  or  blades  set  so  that 
their  center  lines  are  at  right  angles  to  an  axis 
and  their  planes  inclined  at  an  angle  to  the  axis. 
When  the  blades  are  made  to  revolve  about  the 
axis  the  air  is  forced  forward  by  the  action  of 
the  disks  or  blades,  in  the  direction  of  the  axis. 
The  planes  of  the  blades  really  form  parts  of 
helicies,  and  these  helicies  move  the  air  by  their 
action  on  it. 

It  is  evident  that  as  the  blades  of  a  disk  fan 
are  made  to  revolve,  they  tend  to  create  a  vortex 
just  as  do  the  floats  of  a  centrifugal  fan,  but  not 

180 


DISK    FANS.  181 

to  the  same  degree,  because  the  blades  or  floats 
of  a  centrifugal  fan  are  in  the  same  plane  as  the 
axis,  while  the  blades  of  a  disk  fan  are  in  a  plane 
inclined  to  the  axis.  Fig.  31  represents  diagram  - 
matically  the  relative  position  of  a  blade  and  the 
axis  of  a  disk  fan.  The  upper  drawing  represents 
a  view  looking  at  the  end  of  the  axis,  and  the 
lower  one  represents  a  plan.  In  both  views  A 
represents  the  axis  and  B  the  blade.  The  angle 
which  the  plane  of  the  blade  makes  with  the 
axis  is  X,  shown  in  the  lower  drawing  of  Fig.  31. 
The  blades  are  usually  wider  at  the  outer  end 
than  at  the  end  nearest  the  axis. 

It  is  evident  that  when  the  angle  X  is  zero, 
the  blade  is  in  exactly  the  same  position  in  rela- 
tion to  the  axis  as  the  float  of  the  ordinary  cen- 
trifugal fan.  And  when  the  angle  X  is  90  de- 
grees, the  blade  will  move  through  the  air  edge- 
ways and  have  no  appreciable  effect  in  moving 
the  air.  When  X  is  between  zero  and  90  degrees 
there  are  two  effects  on  the  air:  one  is  the  cen- 
trifugal effect  which  makes  the  air  move  radially 
from  the  center  towards  the  outer  point  of  the 
blades,  and  the  other  is  the  screw  effect  which 
makes  the  air  move  in  the  direction  of  the  axis 
of  the  wheel.  The  angle  which  makes  the  centrifu- 
gal effect  least  and  the  screw  effect  the  greatest 
is  the  one  which  will  give  the  best  results. 

The  ordinary  disk  fan  has  usually  perfectly 
straight,  flat  blades,  but  many  manufacturers 


182 


CENTRIFUGAL    FANS. 


O-A 


-'A 


X 


DISK    FANS.  183 

make  special  disk  fans  which  have  the  blades 
curved  in  different  ways  so  as  to  increase  the 
screw  effect  and  diminish  the  centrifugal  effect. 
In  order  to  reduce  the  centrifugal  effect  with 
straight,  flat  blades  the  blades  are  often  made  to 
revolve  inside  of  a  tube-like'  casing  which  pre- 
vents the  air  from  escaping  at  the  outer  edge  of 
the  blades.  Even  when  this  is  done,  however,  it 
is  found  that  there  is  always  more  or  less  escape  of 
air  from  the  blades  at  the  outer  ends,  and  this 
escape  reduces  the  delivering  capacity  of  the  fan. 
If  the  fan  is  made  to  work  against  a  pressure, 
the  slip  or  leakage  of  the  air  from  the  blades  at 
the  outer  edge  is  increased,  and  if  the  pressure 
be  greater  than  a  certain  amount  it  is  found  that 
the  fan  will  not  deliver  any  air  at  all.  The  air 
will  enter  the  fan  at  or  near  the  axis  and  then  be 
blown  backwards  near  the  outer  edge  of  the  blades ; 
the  air  will  simply  circulate  back  and  forth  through 
the  fan,  entering  at  the  central  part  and  leaving 
at  the  outer  part,  on  the  same  side  as  that  on  which 
it  entered. 

This  circulating  of  the  air  through  the  fan 
without  actually  delivering  any  at  the  place  when 
it  is  to  go,  begins  at  different  pressures  for  differ- 
ent fans,  and  depends  upon  the  shape  of  the  blades, 
their  size,  and  the  angle  which  they  make  with 
the  axis  of  the  fan. 

Disk   fans   may    be    divided    into   two    general 


184  CENTRIFUGAL    FANS. 

classes;    those    having    straight,    flat    blades    and 
those  having  curved  blades. 

Those  having  blades  curved  at  the  outer  edge 
so  that  some  advantage  is  obtained  from  the 
centrifugal  action  are  generally  said  to  be  of  the 
Blackman  type,  because  they  resemble  a  form  of 
fan  first  put  on  the  market  by  the  Blackman  Fan 
Co.  of  England.  Fans  of  this  type  will  work 
against  a  slightly  higher  pressure  and  will  deliver 
more  air  than  fans  of  the  straight,  flat  blade  type. 
It  is  probably  safe  to  say  that  disk  fans  are 
essentially  ventilating  fans  and  should  be  used 
only  for  drawing  air  from  a  practically  free  space- 
and  discharging  it  against  no  resistance.  The 
slightest  resistance  to  the  movement  of  the  air 
either  into  the  fan  or  away  from  it  tends  to  reduce 
the  quantity  of  air  delivered  by  the  fan.  These 
fans  cannot  discharge  air  against  a  wind  pressure 
and  when  used  for  ventilating  purposes  must 
have  the  outlet  leading  from  the  fan  so  arranged 
that  the  wind  cannot  blow  directly  into  it. 

The  number  of  blades  seem  to  have  very  little 
effect  upon  the  results  obtained  by  the  use  of  a 
disk  fan,  and  fans  with  a  few  blades,  say  five  or 
six,  will  give  about  as  good  as,  if  not  slightly 
better  results  than,  fans  with  a  larger  number  of 
blades. 

Many  attempts  have  been  made  to  deduce 
theoretical  formulas  for  disk  fans,  but  because  of 
the  great  number  of  variables  that  must  be  con- 


DISK    FANS.  185 

sidered,  and  because  of  the  extreme  mobility  of 
air  and  gases,  the  attempts  can  hardly  be  said  to 
be  successful.  In  all  the  formulas  deduced  there 
have  appeared  certain  terms  or  constants  whose 
values  could  be  determined  only  by  experiment. 
Again  it  seems  probable  that  even  with  a  correct 
and  proper  formula,  any  calculation  made  as  to 
the  working  of  a  disk  fan  must  be  very  carefully 
used  because,  as  has  been  said  before,  a  slight 
resistance  to  the  movement  of  the  air  materially 
affects  the  amount  delivered  by  the  fan,  and  this 
may  be  sufficient  to  upset  all  the  calculations. 

In  1897  Mr.  William  G.  Walker,  of  London, 
read  a  paper  on  Propeller  Fans  before  the  Insti- 
tution of  Mechanical  Engineers,  in  which  he  gave 
the  results  of  a  great  number  of  experiments 
made  by  him  with  disk  fans,  or,  as  he  called  them, 
propeller  fans. 

These  experiments  showed  that  the  best  re- 
sults were  obtained  when  the  blades  of  straight 
blade  disk  fans  were  set  at  an  angle  of  35  or  40 
degrees  with  the  axis. 

They  also  showed  that  the  velocity  of  the  tips 
of  the  blades  was  about  4.35  times  the  mean  veloc- 
ity of  the  air  leaving  the  fan  when  working 
with  a  free,  unobstructed  inlet  and  outlet,  or 
when  working  at  its  maximum  capacity. 

Fig.  32  shows  a  side  view  of  a  disk  fan  which 
is  belt  driven.  The  air  enters  on  the  left  and 
flows  through  the  fan  towards  the  right.  That 


186 


CENTRIFUGAL    FANS. 


CC 
CC 


2 

£ 


NUMBER  OF  REVOLUTIONS  PER  MINUTE.         187 

is  the  air  fllows  into  the  fan  on  the  side  next  to 
the  pulley. 

Fig.  33  shows  a  view  of  the  fan  shown  in 
Fig.  32  when  looking  at  it  from  the  side  on  which 
the  pulley  is.  The  fan  is  supposed  to  be  run 
from  left  to  right,  or  right  handed. 

This  fan  is  arranged  to  be  fastened  before  an 
opening  in  a  wall  so  that  the  air  may  be  taken 
from  a  room  on  one  side  of  the  wall  and  be  dis- 
charged into  a  space  on  the  other  side. 

Number  of  Revolutions  per  Minute.  The  ve- 
locity of  the  tips  of  the  blades  of  a  fan  is  limited 
by  the  strength  of  the  fan,  and  by  the  fact  that 
if  the  velocity  be  too  great  the  fan  will  hum  and 
be  noisy.  There  is  no  danger  of  breaking  and 
little  or  no  noise  if  the  velocity  of  the  tips  of 
the  blades  be  about  5500  feet  per  minute.  Hence 
if  D  be  the  diameter  of  the  fan  in  inches,  and  N 
the  number  of  revolutions  made  by  the  fan  per 
minute,  we  have,  assuming  that  the  velocity  of 
the  tips  of  the  blades  shall  be  5500  feet  per  minute, 

(88)  ^^    -  5500 

From  which  we  get 

(89)  D  N  =  21000 

This  equation  may  be  used  to  determine  the 


188  CENTRIFUGAL    FANS. 

number  of  revolutions  a  disk  fan  of  a  given  diame- 
ter should  make,  and  it  applies  equally  well  to 
all  forms  of  disk  fans. 

Capacity  of  a  Disk  Fan.  The  capacity  of  a  disk 
fan  or  the  number  of  cubic  feet  of  air  which  it 
can  discharge  when  working  with  a  free  inlet 
and  a  free  outlet  may  be  determined  by  equations 
founded  upon  experiments. 

When  a  disk  fan  is  working  freely  the  stream 
of  air  discharged  by  it  is  of  the  same  diameter 
as  the  fan  and  has  a  mean  velocity  which  bears 
a  constant  ratio  to  the  velocity  of  the  tips  of  the 
blades.  If  we  call  this  ratio  x,  we  have  that  the 
mean  velocity  in  feet  per  minute  of  the  stream 
of  air  flowing  from  the  fan  is 

nxDN 


12 


.  The  area  of  cross-section  of  the  stream  is  the 
area  of  a  circle  whose  diameter  is  the  diameter 
of  the  wheel,  that  is  the  area  in  square  feet  is 


nD2 


4X144 


Now    calling    C    the    capacity    of    the    fan    in 
cubic  feet  per  minute  we  have 


(90)  C  = 


CAPACITY  OF  A  DISK  FAN.  189 

X  71*  D*  N 


4x1728 


If  now  we  put  for  D  N  its  value  as  given  by 
(89),  we  get 

x  n2  D2  21000 

4x1728 

-  30.4  x  D2 

From  the  experiments  by  Walker,  already  re- 
ferred to,  we  see  that  for  a  disk  fan  with  plane 
straight  blades  set  at  an  angle  of  about  40  degrees 

with  the  axis,  x    is    equal    to  -TIT^-.    Hence  the 
capacity  of  such  a  fan  is 


From  the  results  of  experiments  quoted  by 
Mr.  Geo.  E.  Babcock  in  the  Transactions  of  the 
American  Society  of  Mechanical  Engineers,  Vol. 
VII.,  1886,  it  is  found  that  x  for  a  disk  fan  of  the 

Blackman    type    is  Hence  the  capacity  of 

2.o8. 

a  disk  fan   with  curved  blades  of  the  Blackman 
type  is 

(93)     c  =        =llz?2 


190  CENTRIFUGAL    FANS. 

It  must  be  remembered  that  equations  (92) 
and  (93)  are  for  fans  working  with  a  perfectly  free 
inlet  and  also  a  perfectly  free  outlet;  conditions 
which  never  do  and  never  can  exist  in  the  actual 
use  of  a  fan.  How  much  the  amount  of  air 
actually  delivered  under  working  conditions  will 
be  less  than*  that  given  by  the  equations  it  is 
impossible  to  predict,  although  it  is  probable 
that  the  air  delivered  by  a  disk  fan  under  ordinary 
good  working  conditions  may  be  taken  as  about 
two  thirds  of  the  capacity  as  given  by  either  (92) 
or  (93). 

That  is  we  may  say  that  under  ordinary  working 
conditions  the  working  capacity  or  C'  is 

f     .    rt        j  5  D2  for  a  straight  blade  disk  fan. 
(  7  D2  for  a  Blackman  type  fan. 


Horse  Power  Required.  The  result  of  Walker's 
experiments  show  that  the  work  required  to  run 
a  disk  fan  is  about  three  times  the  work  required 
to  give  the  mean  velocity  of  the  leaving  stream 
to  the  air  delivered.  And  the  mean  velocity  of 
the  leaving  air  is,  for  fans  with  straight  blades 
from  Walker's  experiments,  equal  to  the  velocity 
of  the  tips  of  the  blades  divided  by  4.35;  and  for 
fans  of  the  Blackman  type,  from  the  experiments 
quoted  by  Babcock,  equal  to  the  velocity  of  the 
tips  of  the  blades  divided  by  2.68. 


HORSE    POWER    REQUIRED.  '  191 

We  have  supposed  that  the  velocity  of  the 
tips  of  the  blades  shall  be  5500  feet  per  minute, 
and  hence  the  mean  velocity  of  the  air  leaving 
the  fan,  in  the  case  of  a  fan  with  straight  blades,  is 


and  in  the  case  of  a  fan  of  the  Blackman  type  it  is 
5500 


2.68 


=  2050. 


For  a  fan  with  straight  blades  the  pressure  in 
ounces  corresponding  to  a  velocity  of  1260  feet 
per  minute,  from  (5),  is 


V=/1260V 


5200  /       \5200  / 
-  0.059 


And  for  a  fan  of  the  Blackman  type  the  pres- 
sure in  ounces  corresponding  to  a  velocity  of  2050 
feet  per  minute,  from  (5),  is 


_    _ 

~  \5200/        \5200/ 

-  0.155 


192  CENTRIFUGAL    FANS. 

The  work  required  to  give  a  quantity  of  air 
a  certain  velocity  is,  as  has  been  explained,  equal 
to  the  number  of  cubic  feet  of  air  moved  multi- 
plied by  the  pressure  in  pounds  per  square  foot 
corresponding  to  the  velocity  of  the  air.  That 
is  the  work  done  per  minute  to  give  C  cubic  feet 
of  air  per  minute  a  velocity  corresponding  to  a 
pressure  of  p  ounces  per  square  inch  is 

144  C  p 


16 


-=  9C> 


And  the  work  per  minute  divided  by  33,000 
gives  the  horse  power. 

For  a  straight  blade  disk  fan  p  has  been  shown 
is  0.059,  and  hence  the  horse  power  K  required 
to  give  the  air  its  mean  velocity,  is 

*Cp       9CXQ'059 


~  &5UOO  "        33000 

C 
~  62200 

For  a  fan  of  the  Blackman  type  p  has  been 
shown  to  be  0.155  and  hence  the  horse  power  re- 
quired to  give  the  air  its  mean  velocity  is 

9CX0.155 


33000    "         33000 

C 
23600 


HORSE    POWER    REQUIRED.  193 

The  horse  power  required  to  run  the  fan  is 
from  the  results  of  Walker's  experiments  equal 
to  3K  as  given  by  (95)  and  (96). 

Hence  the  horse  power  H  required  for  a  straight 
blade  disk  fan  is  from  (95) 


If  now  we  put  for  C  in  (97)  its  value  as  given 
by  (92)  we  get 


(98)         H 


62200       62200 
D2 


3000 


about. 


In  the  same  way  from  (96)  and  (93)  we  get 
that  the  horse  power  required  for  a  disk  fan  of 
the  Blackman  type  is 


(99)       H  -  3  K 


23600 
33  D2        D2 


23600       700 


about. 


194  CENTRIFUGAL    FANS. 

Table  XXI.  gives  the  revolutions  per  minute, 
capacity,  working  capacity,  and  horse  power  re- 
quired for  disk  fans  with  straight,  plane  blades, 
as  calculated  by  (89),  (92),  (94),  and  (98). 

Table  XXII.  gives  the  revolutions  per  minute, 
capacity,  working  capacity,  and  horse  power  re- 
quired for  disk  fans  of  the  Blackman  type  as  cal- 
culated by  (89),  (93),  (94),  and  (99). 

It  must  be  remembered  that  Tables  XXI.  and 
XXII.  are  based  upon  the  supposition  that  the 
velocity  of  the  tips  of  the  blades  will  be  equal  to 
5500  feet  per  minute.  If  the  velocity  be  made 
greater  the  amount  of  air  delivered  by  the  fan 
will  be  increased  and  the  horse  power  required  to 
run  the  fan  will  also  be  increased.  That  is  if  the 
fan  be  run  at  a  speed  of  say  6000  feet  per  minute, 
or  10  per  cent,  greater  than  the  speed  used  in  cal- 
culating the  tables,  the  capacity  and  the  working 
capacity  will  both  be  increased  by  10  per  cent., 
but  the  horse  power  will  be  increased  by  about  20 
per  cent.  This  is  so  because  horse  the  power 
varies  as  the  square  of  the  speed  while  the  capa- 
city and  the  working  capacity  vary  only  as  the 
speed. 

An  inspection  of  Tables  XXI.  and  XXII. 
shows  that  in  order  to  deliver  the  same  amount  of 
air,  a  smaller  fan  of  the  Blackman  type  can  be 
used  than  can  be  used  if  the  fan  has  straight 
blades,  but  the  horse  power  required  for  a  Black- 
man fan  will  be  much  greater  than  the  horse  power 


HORSE    POWER    REQUIRED. 


195 


TABLE  XXI. 
Disk  fans  with  straight,  plane  blades. 


Diameter 
of  wheel 
in  inches 

Revolutions 
per  minute 

Capacity 

Working 
capacity 

Horse  power 
required 

18 

1170 

2270 

1620 

0.11 

24 

875 

4040 

2870 

0.18 

30 

700 

6300 

4500 

0.30 

36 

585 

9100 

6500 

0.43 

42 

500 

12300 

8800 

0.59 

48 

435 

16200 

11600 

0  77 

54 

390 

20500 

14600 

0.97 

60 

350 

25300 

18100 

1.20 

66 

320 

30500 

21800 

1.46 

72 

290 

36400 

26000 

1.73 

TABLE  XXII. 
Disk  fans  of  the  Blackman  type. 


Diameter 
of  wheel 
in  inches 

Revolutions 
per  minute 

Capacity 

Working 
capacity 

Horse  power 
required 

18 

1170 

3560 

2270 

0.46 

24 

875 

6350 

4040 

0.82 

30 

700 

9900 

6300 

1.28 

36 

585 

14200 

9100 

1.76 

42 

500 

19400 

12300 

2.52 

48 

435 

25400 

16200 

3.30 

54 

390 

32200 

20500 

4.17 

60 

350 

39700 

25300 

5.15 

66 

320 

48000 

30500 

6.20 

72 

290 

57000 

36400 

7.40 

196  CENTRIFUGAL    FANS. 

required  for  the  fan  with  straight  blades.  This 
is  so  because  the  velocity  of  the  air  leaving  the 
Blackman  fan  is  much  greater  than  the  velocity 
of  the  air  leaving  the  fan  with  straight  blades. 
And  because  of  the  fact  that  the  velocity  of  the  air 
leaving  the  Blackman  fan  is  so  much  greater  than 
the  velocity  of  the  air  leaving  the  fan  with  straight 
blades,  the  Blackman  fan  may  be  used  for  moving 
air  against  low  pressures,  pressures  in  the  neigh- 
borhood of  about  0.10  of  an  ounce  per  square  inch. 


CHAPTER  XIII. 


Choosing  a  Centrifugal  Fan.  The  size  of  wheel 
and  the  proportions  of  the  wheel  and  housing  for  a 
centrifugal  fan  depend  entirely  upon  the  conditions 
under  which  the  fan  is  to  work.  In  all  cases,  how- 
ever, the  diameter  of  the  wheel  and  the  number  of 
revolutions  per  minute  at  which  it  must  be  run  de- 
pend solely  upon  the  quantity  of  air  to  be  delivered 
per  minute  and  the  pressure  against  which  the  fan 
must  work.  The  quantity  of  air  to  be  delivered  per 
minute  is  always  determined  by  the  known  con- 
ditions of  the  problem  in  hand,  and  the  pressure 
against  which  the  fan  must  work  must  be  calculated 
from  the  conditions  under  which  the  air  must  be 
moved.  This  pressure  is  equal  to  the  head  required 
to  give  to  the  air  the  velocity  which  it  has  when  it 
finally  leaves  the  ducts  or  flues  through  which  it  is 
forced  by  the  fan,  plus  the  head  required  to  overcome 
the  resistance  due  to  friction  of  the  air  in  its  passage 
from  the  fan  outlet  to  the  outlets  of  the  flues  or 

197 


198  CENTRIFUGAL  PANS. 

ducts.  If  there  is  any  resistance  to  the  entrance 
of  the  air  into  the  fan,  the  pressure  required  to 
overcome  it  must  also  be  added  to  the  sum  of  the 
other  pressure  in  order  to  get  the  total  pressure 
against  which  the  fan  must  work. 

Having  determined  the  quantity  of  air  to  be 
moved  per  minute  and  also  the  pressure  against 
which  the  fan  must  work,  the  next  thing  to  decide 
is  the  ratio,  r,  of  the  diameter  of  the  inlet  to  the 
diameter  of  the  wheel.  For  comparatively  high 
pressures  choose  a  fan  with  a  small  value  of  r,  and 
for  low  pressure  choose  a  fan  with  a  rather  large 
value  of  r.  For  ordinary  heating  and  ventilating  , 
work  r  should  be  taken  as  0.625  or  0.707,  but  for 
foundry  work  or  for  certain  kinds  of  gas  work  r 
should  be  taken  less  than  0.625.  The  larger  the 
value  of  r  the  smaller  will  be  the  diameter  of  the 
wheel  required,  but  the  greater  will  be  the  horse 
power  required  to  run  the  fan. 

The  value  of  r  will  also  affect  the  size  of  the 
housing. 

Whether  the  fan  shall  be  a  full  housed,  top, 
horizontal  discharge;  or  a  three-quarter  housed, 
bottom,  horizontal  discharge;  or  even  some  other 
style  of  fan  will  depend  upon  the  space  available 
for  the  apparatus,  and  the  peculiarities  of  the 
place  in  which  it  is  to  be  set  up. 

Having  determined  the  quantity  of  air  to  be 
delivered,  the  pressure  in  ounces  per  square  inch 
against  which  the  fan  must  work,  and  the  ratio  of 


CHOOSING  A  CENTRIFUGAL    FAN.  199 

the  diameter  of  the  inlet  to  the  diameter  of  the 
wheel,  then  take  as  the  size  of  wheel  to  be  used,  that 
wheel  which  when  working  at  its  capacity  against 
the  given  pressure  will  deliver  the  required  quantity 
of  air  per  minute.  In  other  words,  the  pressure 
due  to  the  velocity  of  the  tips  of  the  floats  should 
be  equal  to  the  pressure  against  which  the  air 
must  be  delivered. 

The  considerations  which  govern  the  size  and 
proportions  of  a  fan  for  heating  and  ventilating 
work  are  different  from  those  which  are  encoun- 
tered in  mechanical  draft  work,  or  in  work  per- 
taining to  drying,  or  to  the  removal  of  dust  or 
waste  products  from  a  factory,  and  it  is  impossible 
to  discuss  each  different  class  of  work  here.  It 
suffices  to  say  that  if  the  fan  be  chosen  with 
proper  reference  to  the  work  it  is  to  do  and  the 
conditions  under  which  it  is  to  be  run,  and  then 
be  properly  set  up,  it  will  be  found  to  give  most 
satisfactory  results  and  to  require  very  little  care 
or  attention. 


INDEX. 


PAGB. 

AIR,  flow  of 1 

„     horse  power  for 101 

,,     per  horse  power, 138 

,,       ,,        ,,            ,,     equation  for 139 

,,     table  of 142 

„    revolution, 87 

table  of 89 

,,     velocity  of  flow 2 

,,     volume  of  flowing 4 

Area,  blast 74 

BELTS,  table  for  double : 125 

,,  single 125 

width  of . . . ' 124 

Blast  area, 74 

„          ,,  equation  for 76 

„  table  of 77 

Blowers 44 

CAPACITY, , 64 

,,       of  cone  wheels 175 

of  disk  fans 188 

effect  of  outlet  on 78 

,,        equation  for 72 

201 


202  INDEX. 

Capacity,  table  of ,  67 

,,       table  of,  for  cone  wheels 176 

Coefficient  of  discharge 8 

Cone  wheels, 170 

,,           ,,      capacity  of 175 

,,           ,,      equation  for  required  horse  power 175 

,,           ,,      table  of  capacity  of 176 

,,           ,,      table  of  horse  power  required  for 176 

DIMENSIONS  of  housings 159 

Discharge,  coefficient  of 8 

Disk   fans..                                                                              .  180 


EFFICIENCY, 128 

„          equation  for 132 

table  of 132 

Engine  required  for  fan, 115 

,,               ,,            ,,      ,,  equation  for 115 

Exhausters 143 

FAN,  choosing  a  centrifugal 197 

,,  wheel 51 

Fans, 27 

, ,  cone  wheel 1 70 

,,  disk 180 

,,  engine  required  for 115 

,,  first  type  of 29 

,,  Guibal  type  of 36 

,,  horse  power  to  run 108 

, ,  modern  type  of 44 

,,  motor  required  to  run 121 

,,  second  type  of 36 

,,  third  type  of 39 

Floats..                                                                              ...  53 


INDEX.  203 

HOUSINGS, 147 

,,        dimensions  of 15^ 

M        table  dimensions  of  full  housed,  top,  hori- 
zontal discharge  fans 101,  164 

,,        table  dimensions  of  three  quarter  housed, 

bottom  horizontal  discharge  fans 162,  165 

,,         table  dimensions  of  three  quarter  housed, 

top,  horizontal  discharge  fans 163,  166 

,,        width  of 60 

Horse  power,  air  per 138 

,,            ,,        required  for  the  air 101 

,,            ,,        equation  for 139 

,,            ,,        equation  for  cone  wheels 175 

,,            ,,       equation  for  disk  fans 193 

, ,            , ,        equation  for,  with  large  outlet Ill 

,,        required  to  run  fan, 108 

,,            ,,              M         ,,     ,,       ,,  equation 109 

,,     ,,       „  table  of 110 

,,              ,,          ,,     ,,       ,,  with  large  outlet.  .  Ill 

,,        table  of  for  cone  wheels 176 

INLET 60 

MEAN  effective  pressure,  equation 119 

table  of 120 

Motor  required  to  run  fan 121 

OUTLET,  effect  of  size  on  capacity 78 

,,  ,,       ,,      ,,     ,,    horsepower Ill 

,,  ,,       ,,      ,,      ,,     pressure 94 

PRESSURE, 91 

,,         coefficient,  table  of 96 

„         effect  of  size  of  outlet  on 94 

,,        mean  effective,  table  of 120 

,,         necessary  for  required  velocity 11 

,,         and  revolutions,  equation  for 92 

table  of 93 


204  INDEX. 

REVOLUTIONS  and  pressure, 92 

„                 „         ,,       table  of 93 

of  disk  fans 187 

SCROLL,  radii  for 157 

Shaft 168 

,,     rule  for  size 168 

VANES 53 

VELOCITY,  pressure  necessary 11 

Vortex, 15 

,,     with  radial  flow 22 

WIDTH  of  fans 60 

Work. .                                                                             ....  99 


INDEX  TO  TABLES, 


PAGE. 

AIR,  velocity  of,  in  feet  per  minute  for  various  pres- 
sures per  square  inch,  Table  1 4 

„     cubic  feet  delivered  per  revolution,  Table  V.  ...  89 

,,     delivered  per  minute  per  horse  power,  Table  XII  142 

BLAST   areas   in   square    feet    and    square    inches, 

Table  III 77 

Belts,  horse  power  transmitted  by  single,  Table  X.  .  125 

horse  power  transmitted  by  double,  Table  XA.  125 

CAPACITIES  of  fans  whose  inlets  are  0.707  the  diam- 
eters of  the  wheels,  Table  II 71 

,,  of    fans    whose    inlets    are     0.625     the 

diameters  of  the  wheels,  Table  HA 71 

of  cone  wheel  fans,  Table  XIX 176 

Cone  wheels,  capacities  of,  Table  XIX 176 

„  ,,        horse  power  required  to  run,  Table  XX   176 

DISK  fans  with  straight  plane  blades,  Table  XXI 195 

„     of  the  Blackman  type,  Table  XXII 195 

EFFICIENCY  for  different  ratios  of  diameter  of  inlet  to 

diameter  of  fan  wheel,  Table  XI 132 

205 


206  INDEX    TO    TABLES. 


FRACTION,  value  of  ^  ^  /          a26-2  r2,  Table  IV  ....      85 

A* 

^r2 


,  Table  VII....    96 


HORSE  power,  air  delivered  per,  Table  XII 142 

,,  ,,        for  fans  with  inlets  equal  0.707   the 

diameters  of  the  wheels,  Table  VIII.  .  .  11 
,,             ,,        for  fans  with  inlets  equal  0.625  the 

diameters  of  the  wheels,  Table  VI 1 1  A.  .  110 

transmitted  by  sin^e  belts,  Table  X .  .  125 

„  double     „     Table  XA.  125- 

„            ,,       required  for  cone  wheels,  Table  XX. ..  176 
Housings,    dimensions   of,   Tables  XIII,   XIV,    XV, 

XVI,  XVII  and  XVIII 161-166 

PRESSURES,  velocity  of  air  for,  Table  1 3 

„            number  of  revolutions  for,  Table  VI ....  93 

mean  effective,  Table  IX 120 

REVOLUTIONS     required     for     different     pressures, 

Table  VI 93 

VELOCITY  of  air  for  different  pressures.   Table  I 


